linear_algebra.lagrange | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

70fd9563

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

b5ad1414

bump to nightly-2024-04-28-08

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

4a837c64

Diff

@@ -645,7 +645,7 @@ variable [DecidableEq ι]
 #print Lagrange.nodal_erase_eq_nodal_div /-
 theorem nodal_erase_eq_nodal_div (hi : i ∈ s) : nodal (s.eraseₓ i) v = nodal s v / (X - C (v i)) :=
   by
-  rw [nodal_eq_mul_nodal_erase hi, EuclideanDomain.mul_div_cancel_left]
+  rw [nodal_eq_mul_nodal_erase hi, mul_div_cancel_left₀]
   exact X_sub_C_ne_zero _
 #align lagrange.nodal_erase_eq_nodal_div Lagrange.nodal_erase_eq_nodal_div
 -/

b5ad1414

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -52,8 +52,8 @@ variable (s : Finset R)
 theorem eq_zero_of_degree_lt_of_eval_finset_eq_zero (degree_f_lt : f.degree < s.card)
     (eval_f : ∀ x ∈ s, f.eval x = 0) : f = 0 :=
   by
-  rw [← mem_degree_lt] at degree_f_lt 
-  simp_rw [eval_eq_sum_degree_lt_equiv degree_f_lt] at eval_f 
+  rw [← mem_degree_lt] at degree_f_lt
+  simp_rw [eval_eq_sum_degree_lt_equiv degree_f_lt] at eval_f
   rw [← degree_lt_equiv_eq_zero_iff_eq_zero degree_f_lt]
   exact
     Matrix.eq_zero_of_forall_index_sum_mul_pow_eq_zero
@@ -77,7 +77,7 @@ theorem eq_of_degree_sub_lt_of_eval_finset_eq (degree_fg_lt : (f - g).degree < s
 theorem eq_of_degrees_lt_of_eval_finset_eq (degree_f_lt : f.degree < s.card)
     (degree_g_lt : g.degree < s.card) (eval_fg : ∀ x ∈ s, f.eval x = g.eval x) : f = g :=
   by
-  rw [← mem_degree_lt] at degree_f_lt degree_g_lt 
+  rw [← mem_degree_lt] at degree_f_lt degree_g_lt
   refine' eq_of_degree_sub_lt_of_eval_finset_eq _ _ eval_fg
   rw [← mem_degree_lt]; exact Submodule.sub_mem _ degree_f_lt degree_g_lt
 #align polynomial.eq_of_degrees_lt_of_eval_finset_eq Polynomial.eq_of_degrees_lt_of_eval_finset_eq
@@ -95,7 +95,7 @@ variable {ι : Type _} {v : ι → R} (s : Finset ι)
 theorem eq_zero_of_degree_lt_of_eval_index_eq_zero (hvs : Set.InjOn v s)
     (degree_f_lt : f.degree < s.card) (eval_f : ∀ i ∈ s, f.eval (v i) = 0) : f = 0 := by
   classical
-  rw [← card_image_of_inj_on hvs] at degree_f_lt 
+  rw [← card_image_of_inj_on hvs] at degree_f_lt
   refine' eq_zero_of_degree_lt_of_eval_finset_eq_zero _ degree_f_lt _
   intro x hx
   rcases mem_image.mp hx with ⟨_, hj, rfl⟩
@@ -161,7 +161,7 @@ theorem basisDivisor_self : basisDivisor x x = 0 := by
 theorem basisDivisor_inj (hxy : basisDivisor x y = 0) : x = y :=
   by
   simp_rw [basis_divisor, mul_eq_zero, X_sub_C_ne_zero, or_false_iff, C_eq_zero, inv_eq_zero,
-    sub_eq_zero] at hxy 
+    sub_eq_zero] at hxy
   exact hxy
 #align lagrange.basis_divisor_inj Lagrange.basisDivisor_inj
 -/
@@ -501,7 +501,7 @@ def funEquivDegreeLT (hvs : Set.InjOn v s) : degreeLT F s.card ≃ₗ[F] s → F
   left_inv := by
     rintro ⟨f, hf⟩
     simp only [Subtype.mk_eq_mk, Subtype.coe_mk, dite_eq_ite]
-    rw [mem_degree_lt] at hf 
+    rw [mem_degree_lt] at hf
     nth_rw_rhs 1 [eq_interpolate hvs hf]
     exact interpolate_eq_of_values_eq_on _ _ fun _ hi => if_pos hi
   right_inv := by

b5ad1414

bump to nightly-2024-02-01-06

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

5433bded

Diff

@@ -93,7 +93,13 @@ variable {ι : Type _} {v : ι → R} (s : Finset ι)
 
 #print Polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zero /-
 theorem eq_zero_of_degree_lt_of_eval_index_eq_zero (hvs : Set.InjOn v s)
-    (degree_f_lt : f.degree < s.card) (eval_f : ∀ i ∈ s, f.eval (v i) = 0) : f = 0 := by classical
+    (degree_f_lt : f.degree < s.card) (eval_f : ∀ i ∈ s, f.eval (v i) = 0) : f = 0 := by
+  classical
+  rw [← card_image_of_inj_on hvs] at degree_f_lt 
+  refine' eq_zero_of_degree_lt_of_eval_finset_eq_zero _ degree_f_lt _
+  intro x hx
+  rcases mem_image.mp hx with ⟨_, hj, rfl⟩
+  exact eval_f _ hj
 #align polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zero Polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zero
 -/
 
@@ -338,7 +344,11 @@ theorem sum_basis (hvs : Set.InjOn v s) (hs : s.Nonempty) : ∑ j in s, Lagrange
 
 #print Lagrange.basisDivisor_add_symm /-
 theorem basisDivisor_add_symm {x y : F} (hxy : x ≠ y) : basisDivisor x y + basisDivisor y x = 1 :=
-  by classical
+  by
+  classical rw [←
+    sum_basis (Set.injOn_of_injective Function.injective_id _) ⟨x, mem_insert_self _ {y}⟩,
+    sum_insert (not_mem_singleton.mpr hxy), sum_singleton, basis_pair_left hxy,
+    basis_pair_right hxy, id, id]
 #align lagrange.basis_divisor_add_symm Lagrange.basisDivisor_add_symm
 -/
 
@@ -626,7 +636,7 @@ theorem nodal_eq_mul_nodal_erase [DecidableEq ι] (hi : i ∈ s) :
 
 #print Lagrange.X_sub_C_dvd_nodal /-
 theorem X_sub_C_dvd_nodal (v : ι → F) (hi : i ∈ s) : X - C (v i) ∣ nodal s v :=
-  ⟨_, by classical⟩
+  ⟨_, by classical exact nodal_eq_mul_nodal_erase hi⟩
 #align lagrange.X_sub_C_dvd_nodal Lagrange.X_sub_C_dvd_nodal
 -/

b5ad1414

bump to nightly-2024-01-31-06

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

61100fe9

Diff

@@ -93,13 +93,7 @@ variable {ι : Type _} {v : ι → R} (s : Finset ι)
 
 #print Polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zero /-
 theorem eq_zero_of_degree_lt_of_eval_index_eq_zero (hvs : Set.InjOn v s)
-    (degree_f_lt : f.degree < s.card) (eval_f : ∀ i ∈ s, f.eval (v i) = 0) : f = 0 := by
-  classical
-  rw [← card_image_of_inj_on hvs] at degree_f_lt 
-  refine' eq_zero_of_degree_lt_of_eval_finset_eq_zero _ degree_f_lt _
-  intro x hx
-  rcases mem_image.mp hx with ⟨_, hj, rfl⟩
-  exact eval_f _ hj
+    (degree_f_lt : f.degree < s.card) (eval_f : ∀ i ∈ s, f.eval (v i) = 0) : f = 0 := by classical
 #align polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zero Polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zero
 -/
 
@@ -344,11 +338,7 @@ theorem sum_basis (hvs : Set.InjOn v s) (hs : s.Nonempty) : ∑ j in s, Lagrange
 
 #print Lagrange.basisDivisor_add_symm /-
 theorem basisDivisor_add_symm {x y : F} (hxy : x ≠ y) : basisDivisor x y + basisDivisor y x = 1 :=
-  by
-  classical rw [←
-    sum_basis (Set.injOn_of_injective Function.injective_id _) ⟨x, mem_insert_self _ {y}⟩,
-    sum_insert (not_mem_singleton.mpr hxy), sum_singleton, basis_pair_left hxy,
-    basis_pair_right hxy, id, id]
+  by classical
 #align lagrange.basis_divisor_add_symm Lagrange.basisDivisor_add_symm
 -/
 
@@ -636,7 +626,7 @@ theorem nodal_eq_mul_nodal_erase [DecidableEq ι] (hi : i ∈ s) :
 
 #print Lagrange.X_sub_C_dvd_nodal /-
 theorem X_sub_C_dvd_nodal (v : ι → F) (hi : i ∈ s) : X - C (v i) ∣ nodal s v :=
-  ⟨_, by classical exact nodal_eq_mul_nodal_erase hi⟩
+  ⟨_, by classical⟩
 #align lagrange.X_sub_C_dvd_nodal Lagrange.X_sub_C_dvd_nodal
 -/

b5ad1414

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2020 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Wrenna Robson
 -/
-import Mathbin.Algebra.BigOperators.Basic
-import Mathbin.LinearAlgebra.Vandermonde
-import Mathbin.RingTheory.Polynomial.Basic
+import Algebra.BigOperators.Basic
+import LinearAlgebra.Vandermonde
+import RingTheory.Polynomial.Basic
 
 #align_import linear_algebra.lagrange from "leanprover-community/mathlib"@"b5ad141426bb005414324f89719c77c0aa3ec612"

b5ad1414

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Wrenna Robson
-
-! This file was ported from Lean 3 source module linear_algebra.lagrange
-! leanprover-community/mathlib commit b5ad141426bb005414324f89719c77c0aa3ec612
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.BigOperators.Basic
 import Mathbin.LinearAlgebra.Vandermonde
 import Mathbin.RingTheory.Polynomial.Basic
 
+#align_import linear_algebra.lagrange from "leanprover-community/mathlib"@"b5ad141426bb005414324f89719c77c0aa3ec612"
+
 /-!
 # Lagrange interpolation

b5ad1414

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -51,6 +51,7 @@ open Function Fintype
 
 variable (s : Finset R)
 
+#print Polynomial.eq_zero_of_degree_lt_of_eval_finset_eq_zero /-
 theorem eq_zero_of_degree_lt_of_eval_finset_eq_zero (degree_f_lt : f.degree < s.card)
     (eval_f : ∀ x ∈ s, f.eval x = 0) : f = 0 :=
   by
@@ -62,6 +63,7 @@ theorem eq_zero_of_degree_lt_of_eval_finset_eq_zero (degree_f_lt : f.degree < s.
       (injective.comp (embedding.subtype _).inj' (equiv_fin_of_card_eq (card_coe _)).symm.Injective)
       fun _ => eval_f _ (Finset.coe_mem _)
 #align polynomial.eq_zero_of_degree_lt_of_eval_finset_eq_zero Polynomial.eq_zero_of_degree_lt_of_eval_finset_eq_zero
+-/
 
 #print Polynomial.eq_of_degree_sub_lt_of_eval_finset_eq /-
 theorem eq_of_degree_sub_lt_of_eval_finset_eq (degree_fg_lt : (f - g).degree < s.card)
@@ -92,6 +94,7 @@ open Finset
 
 variable {ι : Type _} {v : ι → R} (s : Finset ι)
 
+#print Polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zero /-
 theorem eq_zero_of_degree_lt_of_eval_index_eq_zero (hvs : Set.InjOn v s)
     (degree_f_lt : f.degree < s.card) (eval_f : ∀ i ∈ s, f.eval (v i) = 0) : f = 0 := by
   classical
@@ -101,6 +104,7 @@ theorem eq_zero_of_degree_lt_of_eval_index_eq_zero (hvs : Set.InjOn v s)
   rcases mem_image.mp hx with ⟨_, hj, rfl⟩
   exact eval_f _ hj
 #align polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zero Polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zero
+-/
 
 #print Polynomial.eq_of_degree_sub_lt_of_eval_index_eq /-
 theorem eq_of_degree_sub_lt_of_eval_index_eq (hvs : Set.InjOn v s)
@@ -205,16 +209,20 @@ theorem natDegree_basisDivisor_of_ne (hxy : x ≠ y) : (basisDivisor x y).natDeg
 #align lagrange.nat_degree_basis_divisor_of_ne Lagrange.natDegree_basisDivisor_of_ne
 -/
 
+#print Lagrange.eval_basisDivisor_right /-
 @[simp]
 theorem eval_basisDivisor_right : eval y (basisDivisor x y) = 0 := by
   simp only [basis_divisor, eval_mul, eval_C, eval_sub, eval_X, sub_self, MulZeroClass.mul_zero]
 #align lagrange.eval_basis_divisor_right Lagrange.eval_basisDivisor_right
+-/
 
+#print Lagrange.eval_basisDivisor_left_of_ne /-
 theorem eval_basisDivisor_left_of_ne (hxy : x ≠ y) : eval x (basisDivisor x y) = 1 :=
   by
   simp only [basis_divisor, eval_mul, eval_C, eval_sub, eval_X]
   exact inv_mul_cancel (sub_ne_zero_of_ne hxy)
 #align lagrange.eval_basis_divisor_left_of_ne Lagrange.eval_basisDivisor_left_of_ne
+-/
 
 end BasisDivisor
 
@@ -233,15 +241,19 @@ protected def basis (s : Finset ι) (v : ι → F) (i : ι) : F[X] :=
 #align lagrange.basis Lagrange.basis
 -/
 
+#print Lagrange.basis_empty /-
 @[simp]
 theorem basis_empty : Lagrange.basis ∅ v i = 1 :=
   rfl
 #align lagrange.basis_empty Lagrange.basis_empty
+-/
 
+#print Lagrange.basis_singleton /-
 @[simp]
 theorem basis_singleton (i : ι) : Lagrange.basis {i} v i = 1 := by
   rw [Lagrange.basis, erase_singleton, prod_empty]
 #align lagrange.basis_singleton Lagrange.basis_singleton
+-/
 
 #print Lagrange.basis_pair_left /-
 @[simp]
@@ -268,6 +280,7 @@ theorem basis_ne_zero (hvs : Set.InjOn v s) (hi : i ∈ s) : Lagrange.basis s v
 #align lagrange.basis_ne_zero Lagrange.basis_ne_zero
 -/
 
+#print Lagrange.eval_basis_self /-
 @[simp]
 theorem eval_basis_self (hvs : Set.InjOn v s) (hi : i ∈ s) :
     (Lagrange.basis s v i).eval (v i) = 1 :=
@@ -278,13 +291,16 @@ theorem eval_basis_self (hvs : Set.InjOn v s) (hi : i ∈ s) :
   rcases mem_erase.mp H with ⟨hij, hj⟩
   exact mt (hvs hi hj) hij.symm
 #align lagrange.eval_basis_self Lagrange.eval_basis_self
+-/
 
+#print Lagrange.eval_basis_of_ne /-
 @[simp]
 theorem eval_basis_of_ne (hij : i ≠ j) (hj : j ∈ s) : (Lagrange.basis s v i).eval (v j) = 0 :=
   by
   simp_rw [Lagrange.basis, eval_prod, prod_eq_zero_iff]
   exact ⟨j, ⟨mem_erase.mpr ⟨hij.symm, hj⟩, eval_basis_divisor_right⟩⟩
 #align lagrange.eval_basis_of_ne Lagrange.eval_basis_of_ne
+-/
 
 #print Lagrange.natDegree_basis /-
 @[simp]
@@ -361,19 +377,26 @@ def interpolate (s : Finset ι) (v : ι → F) : (ι → F) →ₗ[F] F[X]
 #align lagrange.interpolate Lagrange.interpolate
 -/
 
+#print Lagrange.interpolate_empty /-
 @[simp]
 theorem interpolate_empty : interpolate ∅ v r = 0 := by rw [interpolate_apply, sum_empty]
 #align lagrange.interpolate_empty Lagrange.interpolate_empty
+-/
 
+#print Lagrange.interpolate_singleton /-
 @[simp]
 theorem interpolate_singleton : interpolate {i} v r = C (r i) := by
   rw [interpolate_apply, sum_singleton, basis_singleton, mul_one]
 #align lagrange.interpolate_singleton Lagrange.interpolate_singleton
+-/
 
+#print Lagrange.interpolate_one /-
 theorem interpolate_one (hvs : Set.InjOn v s) (hs : s.Nonempty) : interpolate s v 1 = 1 := by
   simp_rw [interpolate_apply, Pi.one_apply, map_one, one_mul]; exact sum_basis hvs hs
 #align lagrange.interpolate_one Lagrange.interpolate_one
+-/
 
+#print Lagrange.eval_interpolate_at_node /-
 theorem eval_interpolate_at_node (hvs : Set.InjOn v s) (hi : i ∈ s) :
     eval (v i) (interpolate s v r) = r i :=
   by
@@ -382,7 +405,9 @@ theorem eval_interpolate_at_node (hvs : Set.InjOn v s) (hi : i ∈ s) :
   refine' sum_eq_zero fun j H => _
   rw [eval_basis_of_ne (mem_erase.mp H).1 hi, MulZeroClass.mul_zero]
 #align lagrange.eval_interpolate_at_node Lagrange.eval_interpolate_at_node
+-/
 
+#print Lagrange.degree_interpolate_le /-
 theorem degree_interpolate_le (hvs : Set.InjOn v s) : (interpolate s v r).degree ≤ ↑(s.card - 1) :=
   by
   refine' (degree_sum_le _ _).trans _
@@ -393,7 +418,9 @@ theorem degree_interpolate_le (hvs : Set.InjOn v s) : (interpolate s v r).degree
   · simpa only [hr, map_zero, degree_zero, WithBot.bot_add] using bot_le
   · rw [degree_C hr, zero_add, WithBot.coe_le_coe]
 #align lagrange.degree_interpolate_le Lagrange.degree_interpolate_le
+-/
 
+#print Lagrange.degree_interpolate_lt /-
 theorem degree_interpolate_lt (hvs : Set.InjOn v s) : (interpolate s v r).degree < s.card :=
   by
   rcases eq_empty_or_nonempty s with (rfl | h)
@@ -403,40 +430,54 @@ theorem degree_interpolate_lt (hvs : Set.InjOn v s) : (interpolate s v r).degree
     rw [WithBot.coe_lt_coe]
     exact Nat.sub_lt (nonempty.card_pos h) zero_lt_one
 #align lagrange.degree_interpolate_lt Lagrange.degree_interpolate_lt
+-/
 
+#print Lagrange.degree_interpolate_erase_lt /-
 theorem degree_interpolate_erase_lt (hvs : Set.InjOn v s) (hi : i ∈ s) :
     (interpolate (s.eraseₓ i) v r).degree < ↑(s.card - 1) :=
   by
   rw [← Finset.card_erase_of_mem hi]
   exact degree_interpolate_lt _ (Set.InjOn.mono (coe_subset.mpr (erase_subset _ _)) hvs)
 #align lagrange.degree_interpolate_erase_lt Lagrange.degree_interpolate_erase_lt
+-/
 
+#print Lagrange.values_eq_on_of_interpolate_eq /-
 theorem values_eq_on_of_interpolate_eq (hvs : Set.InjOn v s)
     (hrr' : interpolate s v r = interpolate s v r') : ∀ i ∈ s, r i = r' i := fun _ hi => by
   rw [← eval_interpolate_at_node r hvs hi, hrr', eval_interpolate_at_node r' hvs hi]
 #align lagrange.values_eq_on_of_interpolate_eq Lagrange.values_eq_on_of_interpolate_eq
+-/
 
+#print Lagrange.interpolate_eq_of_values_eq_on /-
 theorem interpolate_eq_of_values_eq_on (hrr' : ∀ i ∈ s, r i = r' i) :
     interpolate s v r = interpolate s v r' :=
   sum_congr rfl fun i hi => by rw [hrr' _ hi]
 #align lagrange.interpolate_eq_of_values_eq_on Lagrange.interpolate_eq_of_values_eq_on
+-/
 
+#print Lagrange.interpolate_eq_iff_values_eq_on /-
 theorem interpolate_eq_iff_values_eq_on (hvs : Set.InjOn v s) :
     interpolate s v r = interpolate s v r' ↔ ∀ i ∈ s, r i = r' i :=
   ⟨values_eq_on_of_interpolate_eq _ _ hvs, interpolate_eq_of_values_eq_on _ _⟩
 #align lagrange.interpolate_eq_iff_values_eq_on Lagrange.interpolate_eq_iff_values_eq_on
+-/
 
+#print Lagrange.eq_interpolate /-
 theorem eq_interpolate {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree < s.card) :
     f = interpolate s v fun i => f.eval (v i) :=
   eq_of_degrees_lt_of_eval_index_eq _ hvs degree_f_lt (degree_interpolate_lt _ hvs) fun i hi =>
     (eval_interpolate_at_node _ hvs hi).symm
 #align lagrange.eq_interpolate Lagrange.eq_interpolate
+-/
 
+#print Lagrange.eq_interpolate_of_eval_eq /-
 theorem eq_interpolate_of_eval_eq {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree < s.card)
     (eval_f : ∀ i ∈ s, f.eval (v i) = r i) : f = interpolate s v r := by
   rw [eq_interpolate hvs degree_f_lt]; exact interpolate_eq_of_values_eq_on _ _ eval_f
 #align lagrange.eq_interpolate_of_eval_eq Lagrange.eq_interpolate_of_eval_eq
+-/
 
+#print Lagrange.eq_interpolate_iff /-
 /-- This is the characteristic property of the interpolation: the interpolation is the
 unique polynomial of `degree < fintype.card ι` which takes the value of the `r i` on the `v i`.
 -/
@@ -447,6 +488,7 @@ theorem eq_interpolate_iff {f : F[X]} (hvs : Set.InjOn v s) :
   · exact eq_interpolate_of_eval_eq _ hvs h.1 h.2
   · rw [h]; exact ⟨degree_interpolate_lt _ hvs, fun _ hi => eval_interpolate_at_node _ hvs hi⟩
 #align lagrange.eq_interpolate_iff Lagrange.eq_interpolate_iff
+-/
 
 #print Lagrange.funEquivDegreeLT /-
 /-- Lagrange interpolation induces isomorphism between functions from `s`
@@ -473,6 +515,7 @@ def funEquivDegreeLT (hvs : Set.InjOn v s) : degreeLT F s.card ≃ₗ[F] s → F
 #align lagrange.fun_equiv_degree_lt Lagrange.funEquivDegreeLT
 -/
 
+#print Lagrange.interpolate_eq_sum_interpolate_insert_sdiff /-
 theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs : s.Nonempty)
     (hst : s ⊆ t) :
     interpolate t v r = ∑ i in s, interpolate (insert i (t \ s)) v r * Lagrange.basis s v i :=
@@ -511,7 +554,9 @@ theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs :
         eval_interpolate_at_node _ (hvt.mono (insert_subset.mpr ⟨hst hj, sdiff_subset _ _⟩))
           (mem_insert.mpr (Or.inr (mem_sdiff.mpr ⟨hi, hi'⟩)))
 #align lagrange.interpolate_eq_sum_interpolate_insert_sdiff Lagrange.interpolate_eq_sum_interpolate_insert_sdiff
+-/
 
+#print Lagrange.interpolate_eq_add_interpolate_erase /-
 theorem interpolate_eq_add_interpolate_erase (hvs : Set.InjOn v s) (hi : i ∈ s) (hj : j ∈ s)
     (hij : i ≠ j) :
     interpolate s v r =
@@ -526,6 +571,7 @@ theorem interpolate_eq_add_interpolate_erase (hvs : Set.InjOn v s) (hi : i ∈ s
     sdiff_singleton_eq_erase]
   · exact insert_subset.mpr ⟨hi, singleton_subset_iff.mpr hj⟩
 #align lagrange.interpolate_eq_add_interpolate_erase Lagrange.interpolate_eq_add_interpolate_erase
+-/
 
 end Interpolate
 
@@ -548,51 +594,72 @@ def nodal (s : Finset ι) (v : ι → F) : F[X] :=
 #align lagrange.nodal Lagrange.nodal
 -/
 
+#print Lagrange.nodal_eq /-
 theorem nodal_eq (s : Finset ι) (v : ι → F) : nodal s v = ∏ i in s, (X - C (v i)) :=
   rfl
 #align lagrange.nodal_eq Lagrange.nodal_eq
+-/
 
+#print Lagrange.nodal_empty /-
 @[simp]
 theorem nodal_empty : nodal ∅ v = 1 :=
   rfl
 #align lagrange.nodal_empty Lagrange.nodal_empty
+-/
 
+#print Lagrange.degree_nodal /-
 theorem degree_nodal : (nodal s v).degree = s.card := by
   simp_rw [nodal, degree_prod, degree_X_sub_C, sum_const, Nat.smul_one_eq_coe]
 #align lagrange.degree_nodal Lagrange.degree_nodal
+-/
 
+#print Lagrange.eval_nodal /-
 theorem eval_nodal {x : F} : (nodal s v).eval x = ∏ i in s, (x - v i) := by
   simp_rw [nodal, eval_prod, eval_sub, eval_X, eval_C]
 #align lagrange.eval_nodal Lagrange.eval_nodal
+-/
 
+#print Lagrange.eval_nodal_at_node /-
 theorem eval_nodal_at_node (hi : i ∈ s) : eval (v i) (nodal s v) = 0 := by
   rw [eval_nodal, prod_eq_zero_iff]; exact ⟨i, hi, sub_eq_zero_of_eq rfl⟩
 #align lagrange.eval_nodal_at_node Lagrange.eval_nodal_at_node
+-/
 
+#print Lagrange.eval_nodal_not_at_node /-
 theorem eval_nodal_not_at_node (hx : ∀ i ∈ s, x ≠ v i) : eval x (nodal s v) ≠ 0 := by
   simp_rw [nodal, eval_prod, prod_ne_zero_iff, eval_sub, eval_X, eval_C, sub_ne_zero]; exact hx
 #align lagrange.eval_nodal_not_at_node Lagrange.eval_nodal_not_at_node
+-/
 
+#print Lagrange.nodal_eq_mul_nodal_erase /-
 theorem nodal_eq_mul_nodal_erase [DecidableEq ι] (hi : i ∈ s) :
     nodal s v = (X - C (v i)) * nodal (s.eraseₓ i) v := by simp_rw [nodal, mul_prod_erase _ _ hi]
 #align lagrange.nodal_eq_mul_nodal_erase Lagrange.nodal_eq_mul_nodal_erase
+-/
 
+#print Lagrange.X_sub_C_dvd_nodal /-
 theorem X_sub_C_dvd_nodal (v : ι → F) (hi : i ∈ s) : X - C (v i) ∣ nodal s v :=
   ⟨_, by classical exact nodal_eq_mul_nodal_erase hi⟩
 #align lagrange.X_sub_C_dvd_nodal Lagrange.X_sub_C_dvd_nodal
+-/
 
 variable [DecidableEq ι]
 
+#print Lagrange.nodal_erase_eq_nodal_div /-
 theorem nodal_erase_eq_nodal_div (hi : i ∈ s) : nodal (s.eraseₓ i) v = nodal s v / (X - C (v i)) :=
   by
   rw [nodal_eq_mul_nodal_erase hi, EuclideanDomain.mul_div_cancel_left]
   exact X_sub_C_ne_zero _
 #align lagrange.nodal_erase_eq_nodal_div Lagrange.nodal_erase_eq_nodal_div
+-/
 
+#print Lagrange.nodal_insert_eq_nodal /-
 theorem nodal_insert_eq_nodal (hi : i ∉ s) : nodal (insert i s) v = (X - C (v i)) * nodal s v := by
   simp_rw [nodal, prod_insert hi]
 #align lagrange.nodal_insert_eq_nodal Lagrange.nodal_insert_eq_nodal
+-/
 
+#print Lagrange.derivative_nodal /-
 theorem derivative_nodal : (nodal s v).derivative = ∑ i in s, nodal (s.eraseₓ i) v :=
   by
   refine' Finset.induction_on s _ fun _ _ hit IH => _
@@ -603,7 +670,9 @@ theorem derivative_nodal : (nodal s v).derivative = ∑ i in s, nodal (s.erase
     rw [nodal_erase_eq_nodal_div (mem_insert_of_mem hjt), nodal_insert_eq_nodal hit,
       EuclideanDomain.mul_div_assoc _ (X_sub_C_dvd_nodal v hjt), nodal_erase_eq_nodal_div hjt]
 #align lagrange.derivative_nodal Lagrange.derivative_nodal
+-/
 
+#print Lagrange.eval_nodal_derivative_eval_node_eq /-
 theorem eval_nodal_derivative_eval_node_eq (hi : i ∈ s) :
     eval (v i) (nodal s v).derivative = eval (v i) (nodal (s.eraseₓ i) v) :=
   by
@@ -612,6 +681,7 @@ theorem eval_nodal_derivative_eval_node_eq (hi : i ∈ s) :
   simp_rw [nodal, eval_prod, eval_sub, eval_X, eval_C, prod_eq_zero_iff, mem_erase]
   exact ⟨i, ⟨(mem_erase.mp hj).1.symm, hi⟩, sub_eq_zero_of_eq rfl⟩
 #align lagrange.eval_nodal_derivative_eval_node_eq Lagrange.eval_nodal_derivative_eval_node_eq
+-/
 
 #print Lagrange.nodalWeight /-
 /-- This defines the nodal weight for a given set of node indexes and node mapping function `v`. -/
@@ -620,16 +690,21 @@ def nodalWeight (s : Finset ι) (v : ι → F) (i : ι) :=
 #align lagrange.nodal_weight Lagrange.nodalWeight
 -/
 
+#print Lagrange.nodalWeight_eq_eval_nodal_erase_inv /-
 theorem nodalWeight_eq_eval_nodal_erase_inv :
     nodalWeight s v i = (eval (v i) (nodal (s.eraseₓ i) v))⁻¹ := by
   rw [eval_nodal, nodal_weight, prod_inv_distrib]
 #align lagrange.nodal_weight_eq_eval_nodal_erase_inv Lagrange.nodalWeight_eq_eval_nodal_erase_inv
+-/
 
+#print Lagrange.nodalWeight_eq_eval_nodal_derative /-
 theorem nodalWeight_eq_eval_nodal_derative (hi : i ∈ s) :
     nodalWeight s v i = (eval (v i) (nodal s v).derivative)⁻¹ := by
   rw [eval_nodal_derivative_eval_node_eq hi, nodal_weight_eq_eval_nodal_erase_inv]
 #align lagrange.nodal_weight_eq_eval_nodal_derative Lagrange.nodalWeight_eq_eval_nodal_derative
+-/
 
+#print Lagrange.nodalWeight_ne_zero /-
 theorem nodalWeight_ne_zero (hvs : Set.InjOn v s) (hi : i ∈ s) : nodalWeight s v i ≠ 0 :=
   by
   rw [nodal_weight, prod_ne_zero_iff]
@@ -637,25 +712,33 @@ theorem nodalWeight_ne_zero (hvs : Set.InjOn v s) (hi : i ∈ s) : nodalWeight s
   rcases mem_erase.mp hj with ⟨hij, hj⟩
   refine' inv_ne_zero (sub_ne_zero_of_ne (mt (hvs.eq_iff hi hj).mp hij.symm))
 #align lagrange.nodal_weight_ne_zero Lagrange.nodalWeight_ne_zero
+-/
 
+#print Lagrange.basis_eq_prod_sub_inv_mul_nodal_div /-
 theorem basis_eq_prod_sub_inv_mul_nodal_div (hi : i ∈ s) :
     Lagrange.basis s v i = C (nodalWeight s v i) * (nodal s v / (X - C (v i))) := by
   simp_rw [Lagrange.basis, basis_divisor, nodal_weight, prod_mul_distrib, map_prod, ←
     nodal_erase_eq_nodal_div hi, nodal]
 #align lagrange.basis_eq_prod_sub_inv_mul_nodal_div Lagrange.basis_eq_prod_sub_inv_mul_nodal_div
+-/
 
+#print Lagrange.eval_basis_not_at_node /-
 theorem eval_basis_not_at_node (hi : i ∈ s) (hxi : x ≠ v i) :
     eval x (Lagrange.basis s v i) = eval x (nodal s v) * (nodalWeight s v i * (x - v i)⁻¹) := by
   rw [mul_comm, basis_eq_prod_sub_inv_mul_nodal_div hi, eval_mul, eval_C, ←
     nodal_erase_eq_nodal_div hi, eval_nodal, eval_nodal, mul_assoc, ← mul_prod_erase _ _ hi, ←
     mul_assoc (x - v i)⁻¹, inv_mul_cancel (sub_ne_zero_of_ne hxi), one_mul]
 #align lagrange.eval_basis_not_at_node Lagrange.eval_basis_not_at_node
+-/
 
+#print Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C /-
 theorem interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C :
     interpolate s v r = ∑ i in s, C (nodalWeight s v i) * (nodal s v / (X - C (v i))) * C (r i) :=
   sum_congr rfl fun j hj => by rw [mul_comm, basis_eq_prod_sub_inv_mul_nodal_div hj]
 #align lagrange.interpolate_eq_nodal_weight_mul_nodal_div_X_sub_C Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C
+-/
 
+#print Lagrange.eval_interpolate_not_at_node /-
 /-- This is the first barycentric form of the Lagrange interpolant. -/
 theorem eval_interpolate_not_at_node (hx : ∀ i ∈ s, x ≠ v i) :
     eval x (interpolate s v r) =
@@ -665,14 +748,18 @@ theorem eval_interpolate_not_at_node (hx : ∀ i ∈ s, x ≠ v i) :
   refine' sum_congr rfl fun i hi => _
   rw [← mul_assoc, mul_comm, eval_basis_not_at_node hi (hx _ hi)]
 #align lagrange.eval_interpolate_not_at_node Lagrange.eval_interpolate_not_at_node
+-/
 
+#print Lagrange.sum_nodalWeight_mul_inv_sub_ne_zero /-
 theorem sum_nodalWeight_mul_inv_sub_ne_zero (hvs : Set.InjOn v s) (hx : ∀ i ∈ s, x ≠ v i)
     (hs : s.Nonempty) : ∑ i in s, nodalWeight s v i * (x - v i)⁻¹ ≠ 0 :=
   @right_ne_zero_of_mul_eq_one _ _ _ (eval x (nodal s v)) _ <| by
     simpa only [Pi.one_apply, interpolate_one hvs hs, eval_one, mul_one] using
       (eval_interpolate_not_at_node 1 hx).symm
 #align lagrange.sum_nodal_weight_mul_inv_sub_ne_zero Lagrange.sum_nodalWeight_mul_inv_sub_ne_zero
+-/
 
+#print Lagrange.eval_interpolate_not_at_node' /-
 /-- This is the second barycentric form of the Lagrange interpolant. -/
 theorem eval_interpolate_not_at_node' (hvs : Set.InjOn v s) (hs : s.Nonempty)
     (hx : ∀ i ∈ s, x ≠ v i) :
@@ -684,6 +771,7 @@ theorem eval_interpolate_not_at_node' (hvs : Set.InjOn v s) (hs : s.Nonempty)
     eval_interpolate_not_at_node r hx, eval_interpolate_not_at_node 1 hx]
   simp only [mul_div_mul_left _ _ (eval_nodal_not_at_node hx), Pi.one_apply, mul_one]
 #align lagrange.eval_interpolate_not_at_node' Lagrange.eval_interpolate_not_at_node'
+-/
 
 end Nodal

b5ad1414

bump to nightly-2023-06-10-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

3fdc57bc

Diff

@@ -311,7 +311,7 @@ theorem degree_basis (hvs : Set.InjOn v s) (hi : i ∈ s) :
 -/
 
 #print Lagrange.sum_basis /-
-theorem sum_basis (hvs : Set.InjOn v s) (hs : s.Nonempty) : (∑ j in s, Lagrange.basis s v j) = 1 :=
+theorem sum_basis (hvs : Set.InjOn v s) (hs : s.Nonempty) : ∑ j in s, Lagrange.basis s v j = 1 :=
   by
   refine' eq_of_degrees_lt_of_eval_index_eq s hvs (lt_of_le_of_lt (degree_sum_le _ _) _) _ _
   · rw [Finset.sup_lt_iff (WithBot.bot_lt_coe s.card)]
@@ -502,7 +502,7 @@ theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs :
       refine' sum_eq_zero fun j hj => _
       rcases mem_erase.mp hj with ⟨hij, hj⟩
       rw [eval_basis_of_ne hij hi', MulZeroClass.mul_zero]
-    · have H : (∑ j in s, eval (v i) (Lagrange.basis s v j)) = 1 := by
+    · have H : ∑ j in s, eval (v i) (Lagrange.basis s v j) = 1 := by
         rw [← eval_finset_sum, sum_basis (hvt.mono hst) hs, eval_one]
       rw [← mul_one (r i), ← H, mul_sum]
       refine' sum_congr rfl fun j hj => _
@@ -544,11 +544,11 @@ with appropriate multiplicity.
 We can use `nodal` to define the barycentric forms of the evaluated interpolant.
 -/
 def nodal (s : Finset ι) (v : ι → F) : F[X] :=
-  ∏ i in s, X - C (v i)
+  ∏ i in s, (X - C (v i))
 #align lagrange.nodal Lagrange.nodal
 -/
 
-theorem nodal_eq (s : Finset ι) (v : ι → F) : nodal s v = ∏ i in s, X - C (v i) :=
+theorem nodal_eq (s : Finset ι) (v : ι → F) : nodal s v = ∏ i in s, (X - C (v i)) :=
   rfl
 #align lagrange.nodal_eq Lagrange.nodal_eq
 
@@ -561,7 +561,7 @@ theorem degree_nodal : (nodal s v).degree = s.card := by
   simp_rw [nodal, degree_prod, degree_X_sub_C, sum_const, Nat.smul_one_eq_coe]
 #align lagrange.degree_nodal Lagrange.degree_nodal
 
-theorem eval_nodal {x : F} : (nodal s v).eval x = ∏ i in s, x - v i := by
+theorem eval_nodal {x : F} : (nodal s v).eval x = ∏ i in s, (x - v i) := by
   simp_rw [nodal, eval_prod, eval_sub, eval_X, eval_C]
 #align lagrange.eval_nodal Lagrange.eval_nodal
 
@@ -667,7 +667,7 @@ theorem eval_interpolate_not_at_node (hx : ∀ i ∈ s, x ≠ v i) :
 #align lagrange.eval_interpolate_not_at_node Lagrange.eval_interpolate_not_at_node
 
 theorem sum_nodalWeight_mul_inv_sub_ne_zero (hvs : Set.InjOn v s) (hx : ∀ i ∈ s, x ≠ v i)
-    (hs : s.Nonempty) : (∑ i in s, nodalWeight s v i * (x - v i)⁻¹) ≠ 0 :=
+    (hs : s.Nonempty) : ∑ i in s, nodalWeight s v i * (x - v i)⁻¹ ≠ 0 :=
   @right_ne_zero_of_mul_eq_one _ _ _ (eval x (nodal s v)) _ <| by
     simpa only [Pi.one_apply, interpolate_one hvs hs, eval_one, mul_one] using
       (eval_interpolate_not_at_node 1 hx).symm

b5ad1414

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -95,11 +95,11 @@ variable {ι : Type _} {v : ι → R} (s : Finset ι)
 theorem eq_zero_of_degree_lt_of_eval_index_eq_zero (hvs : Set.InjOn v s)
     (degree_f_lt : f.degree < s.card) (eval_f : ∀ i ∈ s, f.eval (v i) = 0) : f = 0 := by
   classical
-    rw [← card_image_of_inj_on hvs] at degree_f_lt 
-    refine' eq_zero_of_degree_lt_of_eval_finset_eq_zero _ degree_f_lt _
-    intro x hx
-    rcases mem_image.mp hx with ⟨_, hj, rfl⟩
-    exact eval_f _ hj
+  rw [← card_image_of_inj_on hvs] at degree_f_lt 
+  refine' eq_zero_of_degree_lt_of_eval_finset_eq_zero _ degree_f_lt _
+  intro x hx
+  rcases mem_image.mp hx with ⟨_, hj, rfl⟩
+  exact eval_f _ hj
 #align polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zero Polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zero
 
 #print Polynomial.eq_of_degree_sub_lt_of_eval_index_eq /-
@@ -333,9 +333,9 @@ theorem sum_basis (hvs : Set.InjOn v s) (hs : s.Nonempty) : (∑ j in s, Lagrang
 theorem basisDivisor_add_symm {x y : F} (hxy : x ≠ y) : basisDivisor x y + basisDivisor y x = 1 :=
   by
   classical rw [←
-      sum_basis (Set.injOn_of_injective Function.injective_id _) ⟨x, mem_insert_self _ {y}⟩,
-      sum_insert (not_mem_singleton.mpr hxy), sum_singleton, basis_pair_left hxy,
-      basis_pair_right hxy, id, id]
+    sum_basis (Set.injOn_of_injective Function.injective_id _) ⟨x, mem_insert_self _ {y}⟩,
+    sum_insert (not_mem_singleton.mpr hxy), sum_singleton, basis_pair_left hxy,
+    basis_pair_right hxy, id, id]
 #align lagrange.basis_divisor_add_symm Lagrange.basisDivisor_add_symm
 -/
 
@@ -488,7 +488,8 @@ theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs :
         Nat.succ_add_sub_one, zero_add]
     rw [degree_basis (Set.InjOn.mono hst hvt) hi, H, WithBot.coe_add,
       WithBot.add_lt_add_iff_right (@WithBot.coe_ne_bot _ (s.card - 1))]
-    convert degree_interpolate_lt _
+    convert
+      degree_interpolate_lt _
         (hvt.mono (coe_subset.mpr (insert_subset.mpr ⟨hst hi, sdiff_subset _ _⟩)))
     rw [card_insert_of_not_mem (not_mem_sdiff_of_mem_right hi), card_sdiff hst, add_comm]
   · simp_rw [eval_finset_sum, eval_mul]

b5ad1414

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -54,8 +54,8 @@ variable (s : Finset R)
 theorem eq_zero_of_degree_lt_of_eval_finset_eq_zero (degree_f_lt : f.degree < s.card)
     (eval_f : ∀ x ∈ s, f.eval x = 0) : f = 0 :=
   by
-  rw [← mem_degree_lt] at degree_f_lt
-  simp_rw [eval_eq_sum_degree_lt_equiv degree_f_lt] at eval_f
+  rw [← mem_degree_lt] at degree_f_lt 
+  simp_rw [eval_eq_sum_degree_lt_equiv degree_f_lt] at eval_f 
   rw [← degree_lt_equiv_eq_zero_iff_eq_zero degree_f_lt]
   exact
     Matrix.eq_zero_of_forall_index_sum_mul_pow_eq_zero
@@ -78,7 +78,7 @@ theorem eq_of_degree_sub_lt_of_eval_finset_eq (degree_fg_lt : (f - g).degree < s
 theorem eq_of_degrees_lt_of_eval_finset_eq (degree_f_lt : f.degree < s.card)
     (degree_g_lt : g.degree < s.card) (eval_fg : ∀ x ∈ s, f.eval x = g.eval x) : f = g :=
   by
-  rw [← mem_degree_lt] at degree_f_lt degree_g_lt
+  rw [← mem_degree_lt] at degree_f_lt degree_g_lt 
   refine' eq_of_degree_sub_lt_of_eval_finset_eq _ _ eval_fg
   rw [← mem_degree_lt]; exact Submodule.sub_mem _ degree_f_lt degree_g_lt
 #align polynomial.eq_of_degrees_lt_of_eval_finset_eq Polynomial.eq_of_degrees_lt_of_eval_finset_eq
@@ -95,7 +95,7 @@ variable {ι : Type _} {v : ι → R} (s : Finset ι)
 theorem eq_zero_of_degree_lt_of_eval_index_eq_zero (hvs : Set.InjOn v s)
     (degree_f_lt : f.degree < s.card) (eval_f : ∀ i ∈ s, f.eval (v i) = 0) : f = 0 := by
   classical
-    rw [← card_image_of_inj_on hvs] at degree_f_lt
+    rw [← card_image_of_inj_on hvs] at degree_f_lt 
     refine' eq_zero_of_degree_lt_of_eval_finset_eq_zero _ degree_f_lt _
     intro x hx
     rcases mem_image.mp hx with ⟨_, hj, rfl⟩
@@ -118,7 +118,7 @@ theorem eq_of_degrees_lt_of_eval_index_eq (hvs : Set.InjOn v s) (degree_f_lt : f
     (degree_g_lt : g.degree < s.card) (eval_fg : ∀ i ∈ s, f.eval (v i) = g.eval (v i)) : f = g :=
   by
   refine' eq_of_degree_sub_lt_of_eval_index_eq _ hvs _ eval_fg
-  rw [← mem_degree_lt] at degree_f_lt degree_g_lt⊢
+  rw [← mem_degree_lt] at degree_f_lt degree_g_lt ⊢
   exact Submodule.sub_mem _ degree_f_lt degree_g_lt
 #align polynomial.eq_of_degrees_lt_of_eval_index_eq Polynomial.eq_of_degrees_lt_of_eval_index_eq
 -/
@@ -160,7 +160,7 @@ theorem basisDivisor_self : basisDivisor x x = 0 := by
 theorem basisDivisor_inj (hxy : basisDivisor x y = 0) : x = y :=
   by
   simp_rw [basis_divisor, mul_eq_zero, X_sub_C_ne_zero, or_false_iff, C_eq_zero, inv_eq_zero,
-    sub_eq_zero] at hxy
+    sub_eq_zero] at hxy 
   exact hxy
 #align lagrange.basis_divisor_inj Lagrange.basisDivisor_inj
 -/
@@ -462,7 +462,7 @@ def funEquivDegreeLT (hvs : Set.InjOn v s) : degreeLT F s.card ≃ₗ[F] s → F
   left_inv := by
     rintro ⟨f, hf⟩
     simp only [Subtype.mk_eq_mk, Subtype.coe_mk, dite_eq_ite]
-    rw [mem_degree_lt] at hf
+    rw [mem_degree_lt] at hf 
     nth_rw_rhs 1 [eq_interpolate hvs hf]
     exact interpolate_eq_of_values_eq_on _ _ fun _ hi => if_pos hi
   right_inv := by

b5ad1414

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -37,7 +37,7 @@ interpolation, where the values are given by a known function `f`.
 -/
 
 
-open Polynomial BigOperators
+open scoped Polynomial BigOperators
 
 section PolynomialDetermination
 
@@ -63,6 +63,7 @@ theorem eq_zero_of_degree_lt_of_eval_finset_eq_zero (degree_f_lt : f.degree < s.
       fun _ => eval_f _ (Finset.coe_mem _)
 #align polynomial.eq_zero_of_degree_lt_of_eval_finset_eq_zero Polynomial.eq_zero_of_degree_lt_of_eval_finset_eq_zero
 
+#print Polynomial.eq_of_degree_sub_lt_of_eval_finset_eq /-
 theorem eq_of_degree_sub_lt_of_eval_finset_eq (degree_fg_lt : (f - g).degree < s.card)
     (eval_fg : ∀ x ∈ s, f.eval x = g.eval x) : f = g :=
   by
@@ -71,7 +72,9 @@ theorem eq_of_degree_sub_lt_of_eval_finset_eq (degree_fg_lt : (f - g).degree < s
   simp_rw [eval_sub, sub_eq_zero]
   exact eval_fg
 #align polynomial.eq_of_degree_sub_lt_of_eval_finset_eq Polynomial.eq_of_degree_sub_lt_of_eval_finset_eq
+-/
 
+#print Polynomial.eq_of_degrees_lt_of_eval_finset_eq /-
 theorem eq_of_degrees_lt_of_eval_finset_eq (degree_f_lt : f.degree < s.card)
     (degree_g_lt : g.degree < s.card) (eval_fg : ∀ x ∈ s, f.eval x = g.eval x) : f = g :=
   by
@@ -79,6 +82,7 @@ theorem eq_of_degrees_lt_of_eval_finset_eq (degree_f_lt : f.degree < s.card)
   refine' eq_of_degree_sub_lt_of_eval_finset_eq _ _ eval_fg
   rw [← mem_degree_lt]; exact Submodule.sub_mem _ degree_f_lt degree_g_lt
 #align polynomial.eq_of_degrees_lt_of_eval_finset_eq Polynomial.eq_of_degrees_lt_of_eval_finset_eq
+-/
 
 end Finset
 
@@ -98,6 +102,7 @@ theorem eq_zero_of_degree_lt_of_eval_index_eq_zero (hvs : Set.InjOn v s)
     exact eval_f _ hj
 #align polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zero Polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zero
 
+#print Polynomial.eq_of_degree_sub_lt_of_eval_index_eq /-
 theorem eq_of_degree_sub_lt_of_eval_index_eq (hvs : Set.InjOn v s)
     (degree_fg_lt : (f - g).degree < s.card) (eval_fg : ∀ i ∈ s, f.eval (v i) = g.eval (v i)) :
     f = g := by
@@ -106,7 +111,9 @@ theorem eq_of_degree_sub_lt_of_eval_index_eq (hvs : Set.InjOn v s)
   simp_rw [eval_sub, sub_eq_zero]
   exact eval_fg
 #align polynomial.eq_of_degree_sub_lt_of_eval_index_eq Polynomial.eq_of_degree_sub_lt_of_eval_index_eq
+-/
 
+#print Polynomial.eq_of_degrees_lt_of_eval_index_eq /-
 theorem eq_of_degrees_lt_of_eval_index_eq (hvs : Set.InjOn v s) (degree_f_lt : f.degree < s.card)
     (degree_g_lt : g.degree < s.card) (eval_fg : ∀ i ∈ s, f.eval (v i) = g.eval (v i)) : f = g :=
   by
@@ -114,6 +121,7 @@ theorem eq_of_degrees_lt_of_eval_index_eq (hvs : Set.InjOn v s) (degree_f_lt : f
   rw [← mem_degree_lt] at degree_f_lt degree_g_lt⊢
   exact Submodule.sub_mem _ degree_f_lt degree_g_lt
 #align polynomial.eq_of_degrees_lt_of_eval_index_eq Polynomial.eq_of_degrees_lt_of_eval_index_eq
+-/
 
 end Indexed

b5ad1414

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -51,12 +51,6 @@ open Function Fintype
 
 variable (s : Finset R)
 
-/- warning: polynomial.eq_zero_of_degree_lt_of_eval_finset_eq_zero -> Polynomial.eq_zero_of_degree_lt_of_eval_finset_eq_zero is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align polynomial.eq_zero_of_degree_lt_of_eval_finset_eq_zero Polynomial.eq_zero_of_degree_lt_of_eval_finset_eq_zeroₓ'. -/
 theorem eq_zero_of_degree_lt_of_eval_finset_eq_zero (degree_f_lt : f.degree < s.card)
     (eval_f : ∀ x ∈ s, f.eval x = 0) : f = 0 :=
   by
@@ -69,12 +63,6 @@ theorem eq_zero_of_degree_lt_of_eval_finset_eq_zero (degree_f_lt : f.degree < s.
       fun _ => eval_f _ (Finset.coe_mem _)
 #align polynomial.eq_zero_of_degree_lt_of_eval_finset_eq_zero Polynomial.eq_zero_of_degree_lt_of_eval_finset_eq_zero
 
-/- warning: polynomial.eq_of_degree_sub_lt_of_eval_finset_eq -> Polynomial.eq_of_degree_sub_lt_of_eval_finset_eq is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align polynomial.eq_of_degree_sub_lt_of_eval_finset_eq Polynomial.eq_of_degree_sub_lt_of_eval_finset_eqₓ'. -/
 theorem eq_of_degree_sub_lt_of_eval_finset_eq (degree_fg_lt : (f - g).degree < s.card)
     (eval_fg : ∀ x ∈ s, f.eval x = g.eval x) : f = g :=
   by
@@ -84,12 +72,6 @@ theorem eq_of_degree_sub_lt_of_eval_finset_eq (degree_fg_lt : (f - g).degree < s
   exact eval_fg
 #align polynomial.eq_of_degree_sub_lt_of_eval_finset_eq Polynomial.eq_of_degree_sub_lt_of_eval_finset_eq
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.eq_of_degrees_lt_of_eval_finset_eq Polynomial.eq_of_degrees_lt_of_eval_finset_eqₓ'. -/
 theorem eq_of_degrees_lt_of_eval_finset_eq (degree_f_lt : f.degree < s.card)
     (degree_g_lt : g.degree < s.card) (eval_fg : ∀ x ∈ s, f.eval x = g.eval x) : f = g :=
   by
@@ -106,12 +88,6 @@ open Finset
 
 variable {ι : Type _} {v : ι → R} (s : Finset ι)
 
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 theorem eq_zero_of_degree_lt_of_eval_index_eq_zero (hvs : Set.InjOn v s)
     (degree_f_lt : f.degree < s.card) (eval_f : ∀ i ∈ s, f.eval (v i) = 0) : f = 0 := by
   classical
@@ -122,12 +98,6 @@ theorem eq_zero_of_degree_lt_of_eval_index_eq_zero (hvs : Set.InjOn v s)
     exact eval_f _ hj
 #align polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zero Polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zero
 
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 theorem eq_of_degree_sub_lt_of_eval_index_eq (hvs : Set.InjOn v s)
     (degree_fg_lt : (f - g).degree < s.card) (eval_fg : ∀ i ∈ s, f.eval (v i) = g.eval (v i)) :
     f = g := by
@@ -137,12 +107,6 @@ theorem eq_of_degree_sub_lt_of_eval_index_eq (hvs : Set.InjOn v s)
   exact eval_fg
 #align polynomial.eq_of_degree_sub_lt_of_eval_index_eq Polynomial.eq_of_degree_sub_lt_of_eval_index_eq
 
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 theorem eq_of_degrees_lt_of_eval_index_eq (hvs : Set.InjOn v s) (degree_f_lt : f.degree < s.card)
     (degree_g_lt : g.degree < s.card) (eval_fg : ∀ i ∈ s, f.eval (v i) = g.eval (v i)) : f = g :=
   by
@@ -233,23 +197,11 @@ theorem natDegree_basisDivisor_of_ne (hxy : x ≠ y) : (basisDivisor x y).natDeg
 #align lagrange.nat_degree_basis_divisor_of_ne Lagrange.natDegree_basisDivisor_of_ne
 -/
 
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 @[simp]
 theorem eval_basisDivisor_right : eval y (basisDivisor x y) = 0 := by
   simp only [basis_divisor, eval_mul, eval_C, eval_sub, eval_X, sub_self, MulZeroClass.mul_zero]
 #align lagrange.eval_basis_divisor_right Lagrange.eval_basisDivisor_right
 
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-Case conversion may be inaccurate. Consider using '#align lagrange.eval_basis_divisor_left_of_ne Lagrange.eval_basisDivisor_left_of_neₓ'. -/
 theorem eval_basisDivisor_left_of_ne (hxy : x ≠ y) : eval x (basisDivisor x y) = 1 :=
   by
   simp only [basis_divisor, eval_mul, eval_C, eval_sub, eval_X]
@@ -273,23 +225,11 @@ protected def basis (s : Finset ι) (v : ι → F) (i : ι) : F[X] :=
 #align lagrange.basis Lagrange.basis
 -/
 
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-Case conversion may be inaccurate. Consider using '#align lagrange.basis_empty Lagrange.basis_emptyₓ'. -/
 @[simp]
 theorem basis_empty : Lagrange.basis ∅ v i = 1 :=
   rfl
 #align lagrange.basis_empty Lagrange.basis_empty
 
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-Case conversion may be inaccurate. Consider using '#align lagrange.basis_singleton Lagrange.basis_singletonₓ'. -/
 @[simp]
 theorem basis_singleton (i : ι) : Lagrange.basis {i} v i = 1 := by
   rw [Lagrange.basis, erase_singleton, prod_empty]
@@ -320,12 +260,6 @@ theorem basis_ne_zero (hvs : Set.InjOn v s) (hi : i ∈ s) : Lagrange.basis s v
 #align lagrange.basis_ne_zero Lagrange.basis_ne_zero
 -/
 
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-Case conversion may be inaccurate. Consider using '#align lagrange.eval_basis_self Lagrange.eval_basis_selfₓ'. -/
 @[simp]
 theorem eval_basis_self (hvs : Set.InjOn v s) (hi : i ∈ s) :
     (Lagrange.basis s v i).eval (v i) = 1 :=
@@ -337,12 +271,6 @@ theorem eval_basis_self (hvs : Set.InjOn v s) (hi : i ∈ s) :
   exact mt (hvs hi hj) hij.symm
 #align lagrange.eval_basis_self Lagrange.eval_basis_self
 
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-Case conversion may be inaccurate. Consider using '#align lagrange.eval_basis_of_ne Lagrange.eval_basis_of_neₓ'. -/
 @[simp]
 theorem eval_basis_of_ne (hij : i ≠ j) (hj : j ∈ s) : (Lagrange.basis s v i).eval (v j) = 0 :=
   by
@@ -425,31 +353,19 @@ def interpolate (s : Finset ι) (v : ι → F) : (ι → F) →ₗ[F] F[X]
 #align lagrange.interpolate Lagrange.interpolate
 -/
 
-/- warning: lagrange.interpolate_empty -> Lagrange.interpolate_empty is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_empty Lagrange.interpolate_emptyₓ'. -/
 @[simp]
 theorem interpolate_empty : interpolate ∅ v r = 0 := by rw [interpolate_apply, sum_empty]
 #align lagrange.interpolate_empty Lagrange.interpolate_empty
 
-/- warning: lagrange.interpolate_singleton -> Lagrange.interpolate_singleton is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_singleton Lagrange.interpolate_singletonₓ'. -/
 @[simp]
 theorem interpolate_singleton : interpolate {i} v r = C (r i) := by
   rw [interpolate_apply, sum_singleton, basis_singleton, mul_one]
 #align lagrange.interpolate_singleton Lagrange.interpolate_singleton
 
-/- warning: lagrange.interpolate_one -> Lagrange.interpolate_one is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_one Lagrange.interpolate_oneₓ'. -/
 theorem interpolate_one (hvs : Set.InjOn v s) (hs : s.Nonempty) : interpolate s v 1 = 1 := by
   simp_rw [interpolate_apply, Pi.one_apply, map_one, one_mul]; exact sum_basis hvs hs
 #align lagrange.interpolate_one Lagrange.interpolate_one
 
-/- warning: lagrange.eval_interpolate_at_node -> Lagrange.eval_interpolate_at_node is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lagrange.eval_interpolate_at_node Lagrange.eval_interpolate_at_nodeₓ'. -/
 theorem eval_interpolate_at_node (hvs : Set.InjOn v s) (hi : i ∈ s) :
     eval (v i) (interpolate s v r) = r i :=
   by
@@ -459,9 +375,6 @@ theorem eval_interpolate_at_node (hvs : Set.InjOn v s) (hi : i ∈ s) :
   rw [eval_basis_of_ne (mem_erase.mp H).1 hi, MulZeroClass.mul_zero]
 #align lagrange.eval_interpolate_at_node Lagrange.eval_interpolate_at_node
 
-/- warning: lagrange.degree_interpolate_le -> Lagrange.degree_interpolate_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lagrange.degree_interpolate_le Lagrange.degree_interpolate_leₓ'. -/
 theorem degree_interpolate_le (hvs : Set.InjOn v s) : (interpolate s v r).degree ≤ ↑(s.card - 1) :=
   by
   refine' (degree_sum_le _ _).trans _
@@ -473,9 +386,6 @@ theorem degree_interpolate_le (hvs : Set.InjOn v s) : (interpolate s v r).degree
   · rw [degree_C hr, zero_add, WithBot.coe_le_coe]
 #align lagrange.degree_interpolate_le Lagrange.degree_interpolate_le
 
-/- warning: lagrange.degree_interpolate_lt -> Lagrange.degree_interpolate_lt is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lagrange.degree_interpolate_lt Lagrange.degree_interpolate_ltₓ'. -/
 theorem degree_interpolate_lt (hvs : Set.InjOn v s) : (interpolate s v r).degree < s.card :=
   by
   rcases eq_empty_or_nonempty s with (rfl | h)
@@ -486,9 +396,6 @@ theorem degree_interpolate_lt (hvs : Set.InjOn v s) : (interpolate s v r).degree
     exact Nat.sub_lt (nonempty.card_pos h) zero_lt_one
 #align lagrange.degree_interpolate_lt Lagrange.degree_interpolate_lt
 
-/- warning: lagrange.degree_interpolate_erase_lt -> Lagrange.degree_interpolate_erase_lt is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lagrange.degree_interpolate_erase_lt Lagrange.degree_interpolate_erase_ltₓ'. -/
 theorem degree_interpolate_erase_lt (hvs : Set.InjOn v s) (hi : i ∈ s) :
     (interpolate (s.eraseₓ i) v r).degree < ↑(s.card - 1) :=
   by
@@ -496,50 +403,32 @@ theorem degree_interpolate_erase_lt (hvs : Set.InjOn v s) (hi : i ∈ s) :
   exact degree_interpolate_lt _ (Set.InjOn.mono (coe_subset.mpr (erase_subset _ _)) hvs)
 #align lagrange.degree_interpolate_erase_lt Lagrange.degree_interpolate_erase_lt
 
-/- warning: lagrange.values_eq_on_of_interpolate_eq -> Lagrange.values_eq_on_of_interpolate_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lagrange.values_eq_on_of_interpolate_eq Lagrange.values_eq_on_of_interpolate_eqₓ'. -/
 theorem values_eq_on_of_interpolate_eq (hvs : Set.InjOn v s)
     (hrr' : interpolate s v r = interpolate s v r') : ∀ i ∈ s, r i = r' i := fun _ hi => by
   rw [← eval_interpolate_at_node r hvs hi, hrr', eval_interpolate_at_node r' hvs hi]
 #align lagrange.values_eq_on_of_interpolate_eq Lagrange.values_eq_on_of_interpolate_eq
 
-/- warning: lagrange.interpolate_eq_of_values_eq_on -> Lagrange.interpolate_eq_of_values_eq_on is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_of_values_eq_on Lagrange.interpolate_eq_of_values_eq_onₓ'. -/
 theorem interpolate_eq_of_values_eq_on (hrr' : ∀ i ∈ s, r i = r' i) :
     interpolate s v r = interpolate s v r' :=
   sum_congr rfl fun i hi => by rw [hrr' _ hi]
 #align lagrange.interpolate_eq_of_values_eq_on Lagrange.interpolate_eq_of_values_eq_on
 
-/- warning: lagrange.interpolate_eq_iff_values_eq_on -> Lagrange.interpolate_eq_iff_values_eq_on is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_iff_values_eq_on Lagrange.interpolate_eq_iff_values_eq_onₓ'. -/
 theorem interpolate_eq_iff_values_eq_on (hvs : Set.InjOn v s) :
     interpolate s v r = interpolate s v r' ↔ ∀ i ∈ s, r i = r' i :=
   ⟨values_eq_on_of_interpolate_eq _ _ hvs, interpolate_eq_of_values_eq_on _ _⟩
 #align lagrange.interpolate_eq_iff_values_eq_on Lagrange.interpolate_eq_iff_values_eq_on
 
-/- warning: lagrange.eq_interpolate -> Lagrange.eq_interpolate is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lagrange.eq_interpolate Lagrange.eq_interpolateₓ'. -/
 theorem eq_interpolate {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree < s.card) :
     f = interpolate s v fun i => f.eval (v i) :=
   eq_of_degrees_lt_of_eval_index_eq _ hvs degree_f_lt (degree_interpolate_lt _ hvs) fun i hi =>
     (eval_interpolate_at_node _ hvs hi).symm
 #align lagrange.eq_interpolate Lagrange.eq_interpolate
 
-/- warning: lagrange.eq_interpolate_of_eval_eq -> Lagrange.eq_interpolate_of_eval_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lagrange.eq_interpolate_of_eval_eq Lagrange.eq_interpolate_of_eval_eqₓ'. -/
 theorem eq_interpolate_of_eval_eq {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree < s.card)
     (eval_f : ∀ i ∈ s, f.eval (v i) = r i) : f = interpolate s v r := by
   rw [eq_interpolate hvs degree_f_lt]; exact interpolate_eq_of_values_eq_on _ _ eval_f
 #align lagrange.eq_interpolate_of_eval_eq Lagrange.eq_interpolate_of_eval_eq
 
-/- warning: lagrange.eq_interpolate_iff -> Lagrange.eq_interpolate_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lagrange.eq_interpolate_iff Lagrange.eq_interpolate_iffₓ'. -/
 /-- This is the characteristic property of the interpolation: the interpolation is the
 unique polynomial of `degree < fintype.card ι` which takes the value of the `r i` on the `v i`.
 -/
@@ -576,9 +465,6 @@ def funEquivDegreeLT (hvs : Set.InjOn v s) : degreeLT F s.card ≃ₗ[F] s → F
 #align lagrange.fun_equiv_degree_lt Lagrange.funEquivDegreeLT
 -/
 
-/- warning: lagrange.interpolate_eq_sum_interpolate_insert_sdiff -> Lagrange.interpolate_eq_sum_interpolate_insert_sdiff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_sum_interpolate_insert_sdiff Lagrange.interpolate_eq_sum_interpolate_insert_sdiffₓ'. -/
 theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs : s.Nonempty)
     (hst : s ⊆ t) :
     interpolate t v r = ∑ i in s, interpolate (insert i (t \ s)) v r * Lagrange.basis s v i :=
@@ -617,9 +503,6 @@ theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs :
           (mem_insert.mpr (Or.inr (mem_sdiff.mpr ⟨hi, hi'⟩)))
 #align lagrange.interpolate_eq_sum_interpolate_insert_sdiff Lagrange.interpolate_eq_sum_interpolate_insert_sdiff
 
-/- warning: lagrange.interpolate_eq_add_interpolate_erase -> Lagrange.interpolate_eq_add_interpolate_erase is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_add_interpolate_erase Lagrange.interpolate_eq_add_interpolate_eraseₓ'. -/
 theorem interpolate_eq_add_interpolate_erase (hvs : Set.InjOn v s) (hi : i ∈ s) (hj : j ∈ s)
     (hij : i ≠ j) :
     interpolate s v r =
@@ -656,99 +539,51 @@ def nodal (s : Finset ι) (v : ι → F) : F[X] :=
 #align lagrange.nodal Lagrange.nodal
 -/
 
-/- warning: lagrange.nodal_eq -> Lagrange.nodal_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lagrange.nodal_eq Lagrange.nodal_eqₓ'. -/
 theorem nodal_eq (s : Finset ι) (v : ι → F) : nodal s v = ∏ i in s, X - C (v i) :=
   rfl
 #align lagrange.nodal_eq Lagrange.nodal_eq
 
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 @[simp]
 theorem nodal_empty : nodal ∅ v = 1 :=
   rfl
 #align lagrange.nodal_empty Lagrange.nodal_empty
 
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 theorem degree_nodal : (nodal s v).degree = s.card := by
   simp_rw [nodal, degree_prod, degree_X_sub_C, sum_const, Nat.smul_one_eq_coe]
 #align lagrange.degree_nodal Lagrange.degree_nodal
 
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 theorem eval_nodal {x : F} : (nodal s v).eval x = ∏ i in s, x - v i := by
   simp_rw [nodal, eval_prod, eval_sub, eval_X, eval_C]
 #align lagrange.eval_nodal Lagrange.eval_nodal
 
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-Case conversion may be inaccurate. Consider using '#align lagrange.eval_nodal_at_node Lagrange.eval_nodal_at_nodeₓ'. -/
 theorem eval_nodal_at_node (hi : i ∈ s) : eval (v i) (nodal s v) = 0 := by
   rw [eval_nodal, prod_eq_zero_iff]; exact ⟨i, hi, sub_eq_zero_of_eq rfl⟩
 #align lagrange.eval_nodal_at_node Lagrange.eval_nodal_at_node
 
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 theorem eval_nodal_not_at_node (hx : ∀ i ∈ s, x ≠ v i) : eval x (nodal s v) ≠ 0 := by
   simp_rw [nodal, eval_prod, prod_ne_zero_iff, eval_sub, eval_X, eval_C, sub_ne_zero]; exact hx
 #align lagrange.eval_nodal_not_at_node Lagrange.eval_nodal_not_at_node
 
-/- warning: lagrange.nodal_eq_mul_nodal_erase -> Lagrange.nodal_eq_mul_nodal_erase is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lagrange.nodal_eq_mul_nodal_erase Lagrange.nodal_eq_mul_nodal_eraseₓ'. -/
 theorem nodal_eq_mul_nodal_erase [DecidableEq ι] (hi : i ∈ s) :
     nodal s v = (X - C (v i)) * nodal (s.eraseₓ i) v := by simp_rw [nodal, mul_prod_erase _ _ hi]
 #align lagrange.nodal_eq_mul_nodal_erase Lagrange.nodal_eq_mul_nodal_erase
 
-/- warning: lagrange.X_sub_C_dvd_nodal -> Lagrange.X_sub_C_dvd_nodal is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lagrange.X_sub_C_dvd_nodal Lagrange.X_sub_C_dvd_nodalₓ'. -/
 theorem X_sub_C_dvd_nodal (v : ι → F) (hi : i ∈ s) : X - C (v i) ∣ nodal s v :=
   ⟨_, by classical exact nodal_eq_mul_nodal_erase hi⟩
 #align lagrange.X_sub_C_dvd_nodal Lagrange.X_sub_C_dvd_nodal
 
 variable [DecidableEq ι]
 
-/- warning: lagrange.nodal_erase_eq_nodal_div -> Lagrange.nodal_erase_eq_nodal_div is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lagrange.nodal_erase_eq_nodal_div Lagrange.nodal_erase_eq_nodal_divₓ'. -/
 theorem nodal_erase_eq_nodal_div (hi : i ∈ s) : nodal (s.eraseₓ i) v = nodal s v / (X - C (v i)) :=
   by
   rw [nodal_eq_mul_nodal_erase hi, EuclideanDomain.mul_div_cancel_left]
   exact X_sub_C_ne_zero _
 #align lagrange.nodal_erase_eq_nodal_div Lagrange.nodal_erase_eq_nodal_div
 
-/- warning: lagrange.nodal_insert_eq_nodal -> Lagrange.nodal_insert_eq_nodal is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lagrange.nodal_insert_eq_nodal Lagrange.nodal_insert_eq_nodalₓ'. -/
 theorem nodal_insert_eq_nodal (hi : i ∉ s) : nodal (insert i s) v = (X - C (v i)) * nodal s v := by
   simp_rw [nodal, prod_insert hi]
 #align lagrange.nodal_insert_eq_nodal Lagrange.nodal_insert_eq_nodal
 
-/- warning: lagrange.derivative_nodal -> Lagrange.derivative_nodal is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lagrange.derivative_nodal Lagrange.derivative_nodalₓ'. -/
 theorem derivative_nodal : (nodal s v).derivative = ∑ i in s, nodal (s.eraseₓ i) v :=
   by
   refine' Finset.induction_on s _ fun _ _ hit IH => _
@@ -760,9 +595,6 @@ theorem derivative_nodal : (nodal s v).derivative = ∑ i in s, nodal (s.erase
       EuclideanDomain.mul_div_assoc _ (X_sub_C_dvd_nodal v hjt), nodal_erase_eq_nodal_div hjt]
 #align lagrange.derivative_nodal Lagrange.derivative_nodal
 
-/- warning: lagrange.eval_nodal_derivative_eval_node_eq -> Lagrange.eval_nodal_derivative_eval_node_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lagrange.eval_nodal_derivative_eval_node_eq Lagrange.eval_nodal_derivative_eval_node_eqₓ'. -/
 theorem eval_nodal_derivative_eval_node_eq (hi : i ∈ s) :
     eval (v i) (nodal s v).derivative = eval (v i) (nodal (s.eraseₓ i) v) :=
   by
@@ -779,31 +611,16 @@ def nodalWeight (s : Finset ι) (v : ι → F) (i : ι) :=
 #align lagrange.nodal_weight Lagrange.nodalWeight
 -/
 
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 theorem nodalWeight_eq_eval_nodal_erase_inv :
     nodalWeight s v i = (eval (v i) (nodal (s.eraseₓ i) v))⁻¹ := by
   rw [eval_nodal, nodal_weight, prod_inv_distrib]
 #align lagrange.nodal_weight_eq_eval_nodal_erase_inv Lagrange.nodalWeight_eq_eval_nodal_erase_inv
 
-/- warning: lagrange.nodal_weight_eq_eval_nodal_derative -> Lagrange.nodalWeight_eq_eval_nodal_derative is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lagrange.nodal_weight_eq_eval_nodal_derative Lagrange.nodalWeight_eq_eval_nodal_derativeₓ'. -/
 theorem nodalWeight_eq_eval_nodal_derative (hi : i ∈ s) :
     nodalWeight s v i = (eval (v i) (nodal s v).derivative)⁻¹ := by
   rw [eval_nodal_derivative_eval_node_eq hi, nodal_weight_eq_eval_nodal_erase_inv]
 #align lagrange.nodal_weight_eq_eval_nodal_derative Lagrange.nodalWeight_eq_eval_nodal_derative
 
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-Case conversion may be inaccurate. Consider using '#align lagrange.nodal_weight_ne_zero Lagrange.nodalWeight_ne_zeroₓ'. -/
 theorem nodalWeight_ne_zero (hvs : Set.InjOn v s) (hi : i ∈ s) : nodalWeight s v i ≠ 0 :=
   by
   rw [nodal_weight, prod_ne_zero_iff]
@@ -812,21 +629,12 @@ theorem nodalWeight_ne_zero (hvs : Set.InjOn v s) (hi : i ∈ s) : nodalWeight s
   refine' inv_ne_zero (sub_ne_zero_of_ne (mt (hvs.eq_iff hi hj).mp hij.symm))
 #align lagrange.nodal_weight_ne_zero Lagrange.nodalWeight_ne_zero
 
-/- warning: lagrange.basis_eq_prod_sub_inv_mul_nodal_div -> Lagrange.basis_eq_prod_sub_inv_mul_nodal_div is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lagrange.basis_eq_prod_sub_inv_mul_nodal_div Lagrange.basis_eq_prod_sub_inv_mul_nodal_divₓ'. -/
 theorem basis_eq_prod_sub_inv_mul_nodal_div (hi : i ∈ s) :
     Lagrange.basis s v i = C (nodalWeight s v i) * (nodal s v / (X - C (v i))) := by
   simp_rw [Lagrange.basis, basis_divisor, nodal_weight, prod_mul_distrib, map_prod, ←
     nodal_erase_eq_nodal_div hi, nodal]
 #align lagrange.basis_eq_prod_sub_inv_mul_nodal_div Lagrange.basis_eq_prod_sub_inv_mul_nodal_div
 
-/- warning: lagrange.eval_basis_not_at_node -> Lagrange.eval_basis_not_at_node is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align lagrange.eval_basis_not_at_node Lagrange.eval_basis_not_at_nodeₓ'. -/
 theorem eval_basis_not_at_node (hi : i ∈ s) (hxi : x ≠ v i) :
     eval x (Lagrange.basis s v i) = eval x (nodal s v) * (nodalWeight s v i * (x - v i)⁻¹) := by
   rw [mul_comm, basis_eq_prod_sub_inv_mul_nodal_div hi, eval_mul, eval_C, ←
@@ -834,17 +642,11 @@ theorem eval_basis_not_at_node (hi : i ∈ s) (hxi : x ≠ v i) :
     mul_assoc (x - v i)⁻¹, inv_mul_cancel (sub_ne_zero_of_ne hxi), one_mul]
 #align lagrange.eval_basis_not_at_node Lagrange.eval_basis_not_at_node
 
-/- warning: lagrange.interpolate_eq_nodal_weight_mul_nodal_div_X_sub_C -> Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_nodal_weight_mul_nodal_div_X_sub_C Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_Cₓ'. -/
 theorem interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C :
     interpolate s v r = ∑ i in s, C (nodalWeight s v i) * (nodal s v / (X - C (v i))) * C (r i) :=
   sum_congr rfl fun j hj => by rw [mul_comm, basis_eq_prod_sub_inv_mul_nodal_div hj]
 #align lagrange.interpolate_eq_nodal_weight_mul_nodal_div_X_sub_C Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C
 
-/- warning: lagrange.eval_interpolate_not_at_node -> Lagrange.eval_interpolate_not_at_node is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lagrange.eval_interpolate_not_at_node Lagrange.eval_interpolate_not_at_nodeₓ'. -/
 /-- This is the first barycentric form of the Lagrange interpolant. -/
 theorem eval_interpolate_not_at_node (hx : ∀ i ∈ s, x ≠ v i) :
     eval x (interpolate s v r) =
@@ -855,12 +657,6 @@ theorem eval_interpolate_not_at_node (hx : ∀ i ∈ s, x ≠ v i) :
   rw [← mul_assoc, mul_comm, eval_basis_not_at_node hi (hx _ hi)]
 #align lagrange.eval_interpolate_not_at_node Lagrange.eval_interpolate_not_at_node
 
-/- warning: lagrange.sum_nodal_weight_mul_inv_sub_ne_zero -> Lagrange.sum_nodalWeight_mul_inv_sub_ne_zero is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align lagrange.sum_nodal_weight_mul_inv_sub_ne_zero Lagrange.sum_nodalWeight_mul_inv_sub_ne_zeroₓ'. -/
 theorem sum_nodalWeight_mul_inv_sub_ne_zero (hvs : Set.InjOn v s) (hx : ∀ i ∈ s, x ≠ v i)
     (hs : s.Nonempty) : (∑ i in s, nodalWeight s v i * (x - v i)⁻¹) ≠ 0 :=
   @right_ne_zero_of_mul_eq_one _ _ _ (eval x (nodal s v)) _ <| by
@@ -868,9 +664,6 @@ theorem sum_nodalWeight_mul_inv_sub_ne_zero (hvs : Set.InjOn v s) (hx : ∀ i 
       (eval_interpolate_not_at_node 1 hx).symm
 #align lagrange.sum_nodal_weight_mul_inv_sub_ne_zero Lagrange.sum_nodalWeight_mul_inv_sub_ne_zero
 
-/- warning: lagrange.eval_interpolate_not_at_node' -> Lagrange.eval_interpolate_not_at_node' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lagrange.eval_interpolate_not_at_node' Lagrange.eval_interpolate_not_at_node'ₓ'. -/
 /-- This is the second barycentric form of the Lagrange interpolant. -/
 theorem eval_interpolate_not_at_node' (hvs : Set.InjOn v s) (hs : s.Nonempty)
     (hx : ∀ i ∈ s, x ≠ v i) :

b5ad1414

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -305,10 +305,8 @@ theorem basis_pair_left (hij : i ≠ j) : Lagrange.basis {i, j} v i = basisDivis
 
 #print Lagrange.basis_pair_right /-
 @[simp]
-theorem basis_pair_right (hij : i ≠ j) : Lagrange.basis {i, j} v j = basisDivisor (v j) (v i) :=
-  by
-  rw [pair_comm]
-  exact basis_pair_left hij.symm
+theorem basis_pair_right (hij : i ≠ j) : Lagrange.basis {i, j} v j = basisDivisor (v j) (v i) := by
+  rw [pair_comm]; exact basis_pair_left hij.symm
 #align lagrange.basis_pair_right Lagrange.basis_pair_right
 -/
 
@@ -445,10 +443,8 @@ theorem interpolate_singleton : interpolate {i} v r = C (r i) := by
 /- warning: lagrange.interpolate_one -> Lagrange.interpolate_one is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_one Lagrange.interpolate_oneₓ'. -/
-theorem interpolate_one (hvs : Set.InjOn v s) (hs : s.Nonempty) : interpolate s v 1 = 1 :=
-  by
-  simp_rw [interpolate_apply, Pi.one_apply, map_one, one_mul]
-  exact sum_basis hvs hs
+theorem interpolate_one (hvs : Set.InjOn v s) (hs : s.Nonempty) : interpolate s v 1 = 1 := by
+  simp_rw [interpolate_apply, Pi.one_apply, map_one, one_mul]; exact sum_basis hvs hs
 #align lagrange.interpolate_one Lagrange.interpolate_one
 
 /- warning: lagrange.eval_interpolate_at_node -> Lagrange.eval_interpolate_at_node is a dubious translation:
@@ -537,10 +533,8 @@ theorem eq_interpolate {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree
 <too large>
 Case conversion may be inaccurate. Consider using '#align lagrange.eq_interpolate_of_eval_eq Lagrange.eq_interpolate_of_eval_eqₓ'. -/
 theorem eq_interpolate_of_eval_eq {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree < s.card)
-    (eval_f : ∀ i ∈ s, f.eval (v i) = r i) : f = interpolate s v r :=
-  by
-  rw [eq_interpolate hvs degree_f_lt]
-  exact interpolate_eq_of_values_eq_on _ _ eval_f
+    (eval_f : ∀ i ∈ s, f.eval (v i) = r i) : f = interpolate s v r := by
+  rw [eq_interpolate hvs degree_f_lt]; exact interpolate_eq_of_values_eq_on _ _ eval_f
 #align lagrange.eq_interpolate_of_eval_eq Lagrange.eq_interpolate_of_eval_eq
 
 /- warning: lagrange.eq_interpolate_iff -> Lagrange.eq_interpolate_iff is a dubious translation:
@@ -554,8 +548,7 @@ theorem eq_interpolate_iff {f : F[X]} (hvs : Set.InjOn v s) :
   by
   constructor <;> intro h
   · exact eq_interpolate_of_eval_eq _ hvs h.1 h.2
-  · rw [h]
-    exact ⟨degree_interpolate_lt _ hvs, fun _ hi => eval_interpolate_at_node _ hvs hi⟩
+  · rw [h]; exact ⟨degree_interpolate_lt _ hvs, fun _ hi => eval_interpolate_at_node _ hvs hi⟩
 #align lagrange.eq_interpolate_iff Lagrange.eq_interpolate_iff
 
 #print Lagrange.funEquivDegreeLT /-
@@ -707,10 +700,8 @@ lean 3 declaration is
 but is expected to have type
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι}, (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (v i) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)) (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (CommMonoidWithZero.toZero.{u1} F (CommGroupWithZero.toCommMonoidWithZero.{u1} F (Semifield.toCommGroupWithZero.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align lagrange.eval_nodal_at_node Lagrange.eval_nodal_at_nodeₓ'. -/
-theorem eval_nodal_at_node (hi : i ∈ s) : eval (v i) (nodal s v) = 0 :=
-  by
-  rw [eval_nodal, prod_eq_zero_iff]
-  exact ⟨i, hi, sub_eq_zero_of_eq rfl⟩
+theorem eval_nodal_at_node (hi : i ∈ s) : eval (v i) (nodal s v) = 0 := by
+  rw [eval_nodal, prod_eq_zero_iff]; exact ⟨i, hi, sub_eq_zero_of_eq rfl⟩
 #align lagrange.eval_nodal_at_node Lagrange.eval_nodal_at_node
 
 /- warning: lagrange.eval_nodal_not_at_node -> Lagrange.eval_nodal_not_at_node is a dubious translation:
@@ -719,10 +710,8 @@ lean 3 declaration is
 but is expected to have type
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {x : F}, (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Ne.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)) (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (CommMonoidWithZero.toZero.{u1} F (CommGroupWithZero.toCommMonoidWithZero.{u1} F (Semifield.toCommGroupWithZero.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align lagrange.eval_nodal_not_at_node Lagrange.eval_nodal_not_at_nodeₓ'. -/
-theorem eval_nodal_not_at_node (hx : ∀ i ∈ s, x ≠ v i) : eval x (nodal s v) ≠ 0 :=
-  by
-  simp_rw [nodal, eval_prod, prod_ne_zero_iff, eval_sub, eval_X, eval_C, sub_ne_zero]
-  exact hx
+theorem eval_nodal_not_at_node (hx : ∀ i ∈ s, x ≠ v i) : eval x (nodal s v) ≠ 0 := by
+  simp_rw [nodal, eval_prod, prod_ne_zero_iff, eval_sub, eval_X, eval_C, sub_ne_zero]; exact hx
 #align lagrange.eval_nodal_not_at_node Lagrange.eval_nodal_not_at_node
 
 /- warning: lagrange.nodal_eq_mul_nodal_erase -> Lagrange.nodal_eq_mul_nodal_erase is a dubious translation:

b5ad1414

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -428,20 +428,14 @@ def interpolate (s : Finset ι) (v : ι → F) : (ι → F) →ₗ[F] F[X]
 -/
 
 /- warning: lagrange.interpolate_empty -> Lagrange.interpolate_empty is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_empty Lagrange.interpolate_emptyₓ'. -/
 @[simp]
 theorem interpolate_empty : interpolate ∅ v r = 0 := by rw [interpolate_apply, sum_empty]
 #align lagrange.interpolate_empty Lagrange.interpolate_empty
 
 /- warning: lagrange.interpolate_singleton -> Lagrange.interpolate_singleton is a dubious translation:
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-but is expected to have type
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+<too large>
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_singleton Lagrange.interpolate_singletonₓ'. -/
 @[simp]
 theorem interpolate_singleton : interpolate {i} v r = C (r i) := by
@@ -449,10 +443,7 @@ theorem interpolate_singleton : interpolate {i} v r = C (r i) := by
 #align lagrange.interpolate_singleton Lagrange.interpolate_singleton
 
 /- warning: lagrange.interpolate_one -> Lagrange.interpolate_one is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_one Lagrange.interpolate_oneₓ'. -/
 theorem interpolate_one (hvs : Set.InjOn v s) (hs : s.Nonempty) : interpolate s v 1 = 1 :=
   by
@@ -461,10 +452,7 @@ theorem interpolate_one (hvs : Set.InjOn v s) (hs : s.Nonempty) : interpolate s
 #align lagrange.interpolate_one Lagrange.interpolate_one
 
 /- warning: lagrange.eval_interpolate_at_node -> Lagrange.eval_interpolate_at_node is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align lagrange.eval_interpolate_at_node Lagrange.eval_interpolate_at_nodeₓ'. -/
 theorem eval_interpolate_at_node (hvs : Set.InjOn v s) (hi : i ∈ s) :
     eval (v i) (interpolate s v r) = r i :=
@@ -476,10 +464,7 @@ theorem eval_interpolate_at_node (hvs : Set.InjOn v s) (hi : i ∈ s) :
 #align lagrange.eval_interpolate_at_node Lagrange.eval_interpolate_at_node
 
 /- warning: lagrange.degree_interpolate_le -> Lagrange.degree_interpolate_le is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align lagrange.degree_interpolate_le Lagrange.degree_interpolate_leₓ'. -/
 theorem degree_interpolate_le (hvs : Set.InjOn v s) : (interpolate s v r).degree ≤ ↑(s.card - 1) :=
   by
@@ -493,10 +478,7 @@ theorem degree_interpolate_le (hvs : Set.InjOn v s) : (interpolate s v r).degree
 #align lagrange.degree_interpolate_le Lagrange.degree_interpolate_le
 
 /- warning: lagrange.degree_interpolate_lt -> Lagrange.degree_interpolate_lt is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align lagrange.degree_interpolate_lt Lagrange.degree_interpolate_ltₓ'. -/
 theorem degree_interpolate_lt (hvs : Set.InjOn v s) : (interpolate s v r).degree < s.card :=
   by
@@ -509,10 +491,7 @@ theorem degree_interpolate_lt (hvs : Set.InjOn v s) : (interpolate s v r).degree
 #align lagrange.degree_interpolate_lt Lagrange.degree_interpolate_lt
 
 /- warning: lagrange.degree_interpolate_erase_lt -> Lagrange.degree_interpolate_erase_lt is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align lagrange.degree_interpolate_erase_lt Lagrange.degree_interpolate_erase_ltₓ'. -/
 theorem degree_interpolate_erase_lt (hvs : Set.InjOn v s) (hi : i ∈ s) :
     (interpolate (s.eraseₓ i) v r).degree < ↑(s.card - 1) :=
@@ -522,10 +501,7 @@ theorem degree_interpolate_erase_lt (hvs : Set.InjOn v s) (hi : i ∈ s) :
 #align lagrange.degree_interpolate_erase_lt Lagrange.degree_interpolate_erase_lt
 
 /- warning: lagrange.values_eq_on_of_interpolate_eq -> Lagrange.values_eq_on_of_interpolate_eq is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align lagrange.values_eq_on_of_interpolate_eq Lagrange.values_eq_on_of_interpolate_eqₓ'. -/
 theorem values_eq_on_of_interpolate_eq (hvs : Set.InjOn v s)
     (hrr' : interpolate s v r = interpolate s v r') : ∀ i ∈ s, r i = r' i := fun _ hi => by
@@ -533,10 +509,7 @@ theorem values_eq_on_of_interpolate_eq (hvs : Set.InjOn v s)
 #align lagrange.values_eq_on_of_interpolate_eq Lagrange.values_eq_on_of_interpolate_eq
 
 /- warning: lagrange.interpolate_eq_of_values_eq_on -> Lagrange.interpolate_eq_of_values_eq_on is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_of_values_eq_on Lagrange.interpolate_eq_of_values_eq_onₓ'. -/
 theorem interpolate_eq_of_values_eq_on (hrr' : ∀ i ∈ s, r i = r' i) :
     interpolate s v r = interpolate s v r' :=
@@ -544,10 +517,7 @@ theorem interpolate_eq_of_values_eq_on (hrr' : ∀ i ∈ s, r i = r' i) :
 #align lagrange.interpolate_eq_of_values_eq_on Lagrange.interpolate_eq_of_values_eq_on
 
 /- warning: lagrange.interpolate_eq_iff_values_eq_on -> Lagrange.interpolate_eq_iff_values_eq_on is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_iff_values_eq_on Lagrange.interpolate_eq_iff_values_eq_onₓ'. -/
 theorem interpolate_eq_iff_values_eq_on (hvs : Set.InjOn v s) :
     interpolate s v r = interpolate s v r' ↔ ∀ i ∈ s, r i = r' i :=
@@ -555,10 +525,7 @@ theorem interpolate_eq_iff_values_eq_on (hvs : Set.InjOn v s) :
 #align lagrange.interpolate_eq_iff_values_eq_on Lagrange.interpolate_eq_iff_values_eq_on
 
 /- warning: lagrange.eq_interpolate -> Lagrange.eq_interpolate is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align lagrange.eq_interpolate Lagrange.eq_interpolateₓ'. -/
 theorem eq_interpolate {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree < s.card) :
     f = interpolate s v fun i => f.eval (v i) :=
@@ -567,10 +534,7 @@ theorem eq_interpolate {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree
 #align lagrange.eq_interpolate Lagrange.eq_interpolate
 
 /- warning: lagrange.eq_interpolate_of_eval_eq -> Lagrange.eq_interpolate_of_eval_eq is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align lagrange.eq_interpolate_of_eval_eq Lagrange.eq_interpolate_of_eval_eqₓ'. -/
 theorem eq_interpolate_of_eval_eq {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree < s.card)
     (eval_f : ∀ i ∈ s, f.eval (v i) = r i) : f = interpolate s v r :=
@@ -580,10 +544,7 @@ theorem eq_interpolate_of_eval_eq {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt
 #align lagrange.eq_interpolate_of_eval_eq Lagrange.eq_interpolate_of_eval_eq
 
 /- warning: lagrange.eq_interpolate_iff -> Lagrange.eq_interpolate_iff is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align lagrange.eq_interpolate_iff Lagrange.eq_interpolate_iffₓ'. -/
 /-- This is the characteristic property of the interpolation: the interpolation is the
 unique polynomial of `degree < fintype.card ι` which takes the value of the `r i` on the `v i`.
@@ -623,10 +584,7 @@ def funEquivDegreeLT (hvs : Set.InjOn v s) : degreeLT F s.card ≃ₗ[F] s → F
 -/
 
 /- warning: lagrange.interpolate_eq_sum_interpolate_insert_sdiff -> Lagrange.interpolate_eq_sum_interpolate_insert_sdiff is a dubious translation:
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F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Insert.insert.{u2, u2} ι (Finset.{u2} ι) (Finset.instInsertFinset.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) i (SDiff.sdiff.{u2} (Finset.{u2} ι) (Finset.instSDiffFinset.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) t s)) v) r) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_sum_interpolate_insert_sdiff Lagrange.interpolate_eq_sum_interpolate_insert_sdiffₓ'. -/
 theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs : s.Nonempty)
     (hst : s ⊆ t) :
@@ -667,10 +625,7 @@ theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs :
 #align lagrange.interpolate_eq_sum_interpolate_insert_sdiff Lagrange.interpolate_eq_sum_interpolate_insert_sdiff
 
 /- warning: lagrange.interpolate_eq_add_interpolate_erase -> Lagrange.interpolate_eq_add_interpolate_erase is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_add_interpolate_erase Lagrange.interpolate_eq_add_interpolate_eraseₓ'. -/
 theorem interpolate_eq_add_interpolate_erase (hvs : Set.InjOn v s) (hi : i ∈ s) (hj : j ∈ s)
     (hij : i ≠ j) :
@@ -709,10 +664,7 @@ def nodal (s : Finset ι) (v : ι → F) : F[X] :=
 -/
 
 /- warning: lagrange.nodal_eq -> Lagrange.nodal_eq is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align lagrange.nodal_eq Lagrange.nodal_eqₓ'. -/
 theorem nodal_eq (s : Finset ι) (v : ι → F) : nodal s v = ∏ i in s, X - C (v i) :=
   rfl
@@ -774,20 +726,14 @@ theorem eval_nodal_not_at_node (hx : ∀ i ∈ s, x ≠ v i) : eval x (nodal s v
 #align lagrange.eval_nodal_not_at_node Lagrange.eval_nodal_not_at_node
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align lagrange.nodal_eq_mul_nodal_erase Lagrange.nodal_eq_mul_nodal_eraseₓ'. -/
 theorem nodal_eq_mul_nodal_erase [DecidableEq ι] (hi : i ∈ s) :
     nodal s v = (X - C (v i)) * nodal (s.eraseₓ i) v := by simp_rw [nodal, mul_prod_erase _ _ hi]
 #align lagrange.nodal_eq_mul_nodal_erase Lagrange.nodal_eq_mul_nodal_erase
 
 /- warning: lagrange.X_sub_C_dvd_nodal -> Lagrange.X_sub_C_dvd_nodal is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align lagrange.X_sub_C_dvd_nodal Lagrange.X_sub_C_dvd_nodalₓ'. -/
 theorem X_sub_C_dvd_nodal (v : ι → F) (hi : i ∈ s) : X - C (v i) ∣ nodal s v :=
   ⟨_, by classical exact nodal_eq_mul_nodal_erase hi⟩
@@ -796,10 +742,7 @@ theorem X_sub_C_dvd_nodal (v : ι → F) (hi : i ∈ s) : X - C (v i) ∣ nodal
 variable [DecidableEq ι]
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align lagrange.nodal_erase_eq_nodal_div Lagrange.nodal_erase_eq_nodal_divₓ'. -/
 theorem nodal_erase_eq_nodal_div (hi : i ∈ s) : nodal (s.eraseₓ i) v = nodal s v / (X - C (v i)) :=
   by
@@ -808,20 +751,14 @@ theorem nodal_erase_eq_nodal_div (hi : i ∈ s) : nodal (s.eraseₓ i) v = nodal
 #align lagrange.nodal_erase_eq_nodal_div Lagrange.nodal_erase_eq_nodal_div
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align lagrange.nodal_insert_eq_nodal Lagrange.nodal_insert_eq_nodalₓ'. -/
 theorem nodal_insert_eq_nodal (hi : i ∉ s) : nodal (insert i s) v = (X - C (v i)) * nodal s v := by
   simp_rw [nodal, prod_insert hi]
 #align lagrange.nodal_insert_eq_nodal Lagrange.nodal_insert_eq_nodal
 
 /- warning: lagrange.derivative_nodal -> Lagrange.derivative_nodal is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align lagrange.derivative_nodal Lagrange.derivative_nodalₓ'. -/
 theorem derivative_nodal : (nodal s v).derivative = ∑ i in s, nodal (s.eraseₓ i) v :=
   by
@@ -835,10 +772,7 @@ theorem derivative_nodal : (nodal s v).derivative = ∑ i in s, nodal (s.erase
 #align lagrange.derivative_nodal Lagrange.derivative_nodal
 
 /- warning: lagrange.eval_nodal_derivative_eval_node_eq -> Lagrange.eval_nodal_derivative_eval_node_eq is a dubious translation:
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(DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.derivative.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v))) (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) (Lagrange.nodal.{u1, u2} F _inst_1 ι (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v)))
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(DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F 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+<too large>
 Case conversion may be inaccurate. Consider using '#align lagrange.eval_nodal_derivative_eval_node_eq Lagrange.eval_nodal_derivative_eval_node_eqₓ'. -/
 theorem eval_nodal_derivative_eval_node_eq (hi : i ∈ s) :
     eval (v i) (nodal s v).derivative = eval (v i) (nodal (s.eraseₓ i) v) :=
@@ -868,10 +802,7 @@ theorem nodalWeight_eq_eval_nodal_erase_inv :
 #align lagrange.nodal_weight_eq_eval_nodal_erase_inv Lagrange.nodalWeight_eq_eval_nodal_erase_inv
 
 /- warning: lagrange.nodal_weight_eq_eval_nodal_derative -> Lagrange.nodalWeight_eq_eval_nodal_derative is a dubious translation:
-lean 3 declaration is
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(Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F 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(DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.derivative.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)))))
-but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u2} ι], (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (v i) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} F F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Polynomial.derivative.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align lagrange.nodal_weight_eq_eval_nodal_derative Lagrange.nodalWeight_eq_eval_nodal_derativeₓ'. -/
 theorem nodalWeight_eq_eval_nodal_derative (hi : i ∈ s) :
     nodalWeight s v i = (eval (v i) (nodal s v).derivative)⁻¹ := by
@@ -893,10 +824,7 @@ theorem nodalWeight_ne_zero (hvs : Set.InjOn v s) (hi : i ∈ s) : nodalWeight s
 #align lagrange.nodal_weight_ne_zero Lagrange.nodalWeight_ne_zero
 
 /- warning: lagrange.basis_eq_prod_sub_inv_mul_nodal_div -> Lagrange.basis_eq_prod_sub_inv_mul_nodal_div is a dubious translation:
-lean 3 declaration is
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(Field.toDivisionRing.{u1} F _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.hasDiv.{u1} F _inst_1)) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (v i))))))
-but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u2} ι], (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F 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_inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F 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F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align lagrange.basis_eq_prod_sub_inv_mul_nodal_div Lagrange.basis_eq_prod_sub_inv_mul_nodal_divₓ'. -/
 theorem basis_eq_prod_sub_inv_mul_nodal_div (hi : i ∈ s) :
     Lagrange.basis s v i = C (nodalWeight s v i) * (nodal s v / (X - C (v i))) := by
@@ -918,10 +846,7 @@ theorem eval_basis_not_at_node (hi : i ∈ s) (hxi : x ≠ v i) :
 #align lagrange.eval_basis_not_at_node Lagrange.eval_basis_not_at_node
 
 /- warning: lagrange.interpolate_eq_nodal_weight_mul_nodal_div_X_sub_C -> Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C is a dubious translation:
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(Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (Finset.sum.{u2, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (NonAssocRing.toNonUnitalNonAssocRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Ring.toNonAssocRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (CommRing.toRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (EuclideanDomain.toCommRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (HDiv.hDiv.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHDiv.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instDivPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1)) (Lagrange.nodal.{u2, u1} F _inst_1 ι s v) (HSub.hSub.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (v i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHSub.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.sub.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (Polynomial.X.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) 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(Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F 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+<too large>
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_nodal_weight_mul_nodal_div_X_sub_C Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_Cₓ'. -/
 theorem interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C :
     interpolate s v r = ∑ i in s, C (nodalWeight s v i) * (nodal s v / (X - C (v i))) * C (r i) :=
@@ -929,10 +854,7 @@ theorem interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C :
 #align lagrange.interpolate_eq_nodal_weight_mul_nodal_div_X_sub_C Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C
 
 /- warning: lagrange.eval_interpolate_not_at_node -> Lagrange.eval_interpolate_not_at_node is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align lagrange.eval_interpolate_not_at_node Lagrange.eval_interpolate_not_at_nodeₓ'. -/
 /-- This is the first barycentric form of the Lagrange interpolant. -/
 theorem eval_interpolate_not_at_node (hx : ∀ i ∈ s, x ≠ v i) :
@@ -958,10 +880,7 @@ theorem sum_nodalWeight_mul_inv_sub_ne_zero (hvs : Set.InjOn v s) (hx : ∀ i 
 #align lagrange.sum_nodal_weight_mul_inv_sub_ne_zero Lagrange.sum_nodalWeight_mul_inv_sub_ne_zero
 
 /- warning: lagrange.eval_interpolate_not_at_node' -> Lagrange.eval_interpolate_not_at_node' is a dubious translation:
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(HDiv.hDiv.{u1, u1, u1} F F F (instHDiv.{u1} F (DivInvMonoid.toHasDiv.{u1} F (DivisionRing.toDivInvMonoid.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Finset.sum.{u1, u2} F ι (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (DivInvMonoid.toHasInv.{u1} F (DivisionRing.toDivInvMonoid.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (HSub.hSub.{u1, u1, u1} F F F 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(SubNegMonoid.toHasSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (AddGroupWithOne.toAddGroup.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))) x (v i)))))))
-but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Finset.Nonempty.{u2} ι s) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F 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(NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) 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(Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HDiv.hDiv.{u1, u1, u1} F F F (instHDiv.{u1} F (Field.toDiv.{u1} F _inst_1)) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F 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+<too large>
 Case conversion may be inaccurate. Consider using '#align lagrange.eval_interpolate_not_at_node' Lagrange.eval_interpolate_not_at_node'ₓ'. -/
 /-- This is the second barycentric form of the Lagrange interpolant. -/
 theorem eval_interpolate_not_at_node' (hvs : Set.InjOn v s) (hs : s.Nonempty)

b5ad1414

bump to nightly-2023-05-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

fbc7b476

Diff

@@ -431,7 +431,7 @@ def interpolate (s : Finset ι) (v : ι → F) : (ι → F) →ₗ[F] F[X]
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {v : ι -> F} (r : ι -> F), Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (EmptyCollection.emptyCollection.{u2} (Finset.{u2} ι) (Finset.hasEmptyc.{u2} ι)) v) r) (OfNat.ofNat.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.zero.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {v : ι -> F} (r : ι -> F), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (EmptyCollection.emptyCollection.{u1} (Finset.{u1} ι) (Finset.instEmptyCollectionFinset.{u1} ι)) v) r) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Polynomial.zero.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {v : ι -> F} (r : ι -> F), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (EmptyCollection.emptyCollection.{u1} (Finset.{u1} ι) (Finset.instEmptyCollectionFinset.{u1} ι)) v) r) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Polynomial.zero.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_empty Lagrange.interpolate_emptyₓ'. -/
 @[simp]
 theorem interpolate_empty : interpolate ∅ v r = 0 := by rw [interpolate_apply, sum_empty]
@@ -441,7 +441,7 @@ theorem interpolate_empty : interpolate ∅ v r = 0 := by rw [interpolate_apply,
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {i : ι} {v : ι -> F} (r : ι -> F), Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Singleton.singleton.{u2, u2} ι (Finset.{u2} ι) (Finset.hasSingleton.{u2} ι) i) v) r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (r i))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {i : ι} {v : ι -> F} (r : ι -> F), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Singleton.singleton.{u1, u1} ι (Finset.{u1} ι) (Finset.instSingletonFinset.{u1} ι) i) v) r) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {i : ι} {v : ι -> F} (r : ι -> F), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Singleton.singleton.{u1, u1} ι (Finset.{u1} ι) (Finset.instSingletonFinset.{u1} ι) i) v) r) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_singleton Lagrange.interpolate_singletonₓ'. -/
 @[simp]
 theorem interpolate_singleton : interpolate {i} v r = C (r i) := by
@@ -452,7 +452,7 @@ theorem interpolate_singleton : interpolate {i} v r = C (r i) := by
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F}, (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Finset.Nonempty.{u2} ι s) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (OfNat.ofNat.{max u2 u1} (ι -> F) 1 (OfNat.mk.{max u2 u1} (ι -> F) 1 (One.one.{max u2 u1} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddMonoidWithOne.toOne.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) (OfNat.ofNat.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 1 (OfNat.mk.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 1 (One.one.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.hasOne.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F}, (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Finset.Nonempty.{u2} ι s) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Polynomial.one.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F}, (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Finset.Nonempty.{u2} ι s) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Polynomial.one.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_one Lagrange.interpolate_oneₓ'. -/
 theorem interpolate_one (hvs : Set.InjOn v s) (hs : s.Nonempty) : interpolate s v 1 = 1 :=
   by
@@ -464,7 +464,7 @@ theorem interpolate_one (hvs : Set.InjOn v s) (hs : s.Nonempty) : interpolate s
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (r i))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (v i) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (r i))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (v i) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (r i))
 Case conversion may be inaccurate. Consider using '#align lagrange.eval_interpolate_at_node Lagrange.eval_interpolate_at_nodeₓ'. -/
 theorem eval_interpolate_at_node (hvs : Set.InjOn v s) (hi : i ∈ s) :
     eval (v i) (interpolate s v r) = r i :=
@@ -479,7 +479,7 @@ theorem eval_interpolate_at_node (hvs : Set.InjOn v s) (hi : i ∈ s) :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toHasLe.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
 Case conversion may be inaccurate. Consider using '#align lagrange.degree_interpolate_le Lagrange.degree_interpolate_leₓ'. -/
 theorem degree_interpolate_le (hvs : Set.InjOn v s) : (interpolate s v r).degree ≤ ↑(s.card - 1) :=
   by
@@ -496,7 +496,7 @@ theorem degree_interpolate_le (hvs : Set.InjOn v s) : (interpolate s v r).degree
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s)))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u2} ι s)))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u2} ι s)))
 Case conversion may be inaccurate. Consider using '#align lagrange.degree_interpolate_lt Lagrange.degree_interpolate_ltₓ'. -/
 theorem degree_interpolate_lt (hvs : Set.InjOn v s) : (interpolate s v r).degree < s.card :=
   by
@@ -512,7 +512,7 @@ theorem degree_interpolate_lt (hvs : Set.InjOn v s) : (interpolate s v r).degree
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
 Case conversion may be inaccurate. Consider using '#align lagrange.degree_interpolate_erase_lt Lagrange.degree_interpolate_erase_ltₓ'. -/
 theorem degree_interpolate_erase_lt (hvs : Set.InjOn v s) (hi : i ∈ s) :
     (interpolate (s.eraseₓ i) v r).degree < ↑(s.card - 1) :=
@@ -525,7 +525,7 @@ theorem degree_interpolate_erase_lt (hvs : Set.InjOn v s) (hi : i ∈ s) :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F 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(DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i)))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i)))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i)))
 Case conversion may be inaccurate. Consider using '#align lagrange.values_eq_on_of_interpolate_eq Lagrange.values_eq_on_of_interpolate_eqₓ'. -/
 theorem values_eq_on_of_interpolate_eq (hvs : Set.InjOn v s)
     (hrr' : interpolate s v r = interpolate s v r') : ∀ i ∈ s, r i = r' i := fun _ hi => by
@@ -536,7 +536,7 @@ theorem values_eq_on_of_interpolate_eq (hvs : Set.InjOn v s)
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r'))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r'))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r'))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_of_values_eq_on Lagrange.interpolate_eq_of_values_eq_onₓ'. -/
 theorem interpolate_eq_of_values_eq_on (hrr' : ∀ i ∈ s, r i = r' i) :
     interpolate s v r = interpolate s v r' :=
@@ -547,7 +547,7 @@ theorem interpolate_eq_of_values_eq_on (hrr' : ∀ i ∈ s, r i = r' i) :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Iff (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} 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(Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F 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(Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_iff_values_eq_on Lagrange.interpolate_eq_iff_values_eq_onₓ'. -/
 theorem interpolate_eq_iff_values_eq_on (hvs : Set.InjOn v s) :
     interpolate s v r = interpolate s v r' ↔ ∀ i ∈ s, r i = r' i :=
@@ -558,7 +558,7 @@ theorem interpolate_eq_iff_values_eq_on (hvs : Set.InjOn v s) :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s))) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (fun (i : ι) => Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) f)))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) -> (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (fun (i : ι) => Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f)))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) -> (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (fun (i : ι) => Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f)))
 Case conversion may be inaccurate. Consider using '#align lagrange.eq_interpolate Lagrange.eq_interpolateₓ'. -/
 theorem eq_interpolate {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree < s.card) :
     f = interpolate s v fun i => f.eval (v i) :=
@@ -570,7 +570,7 @@ theorem eq_interpolate {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s))) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) f) (r i))) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u2} F (Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f) (r i))) -> (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u2} F (Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f) (r i))) -> (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r))
 Case conversion may be inaccurate. Consider using '#align lagrange.eq_interpolate_of_eval_eq Lagrange.eq_interpolate_of_eval_eqₓ'. -/
 theorem eq_interpolate_of_eval_eq {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree < s.card)
     (eval_f : ∀ i ∈ s, f.eval (v i) = r i) : f = interpolate s v r :=
@@ -583,7 +583,7 @@ theorem eq_interpolate_of_eval_eq {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Iff (And (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s))) (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) f) (r i)))) (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (Iff (And (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u2} F (Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f) (r i)))) (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (Iff (And (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u2} F (Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f) (r i)))) (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)))
 Case conversion may be inaccurate. Consider using '#align lagrange.eq_interpolate_iff Lagrange.eq_interpolate_iffₓ'. -/
 /-- This is the characteristic property of the interpolation: the interpolation is the
 unique polynomial of `degree < fintype.card ι` which takes the value of the `r i` on the `v i`.
@@ -626,7 +626,7 @@ def funEquivDegreeLT (hvs : Set.InjOn v s) : degreeLT F s.card ≃ₗ[F] s → F
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {t : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) t)) -> (Finset.Nonempty.{u2} ι s) -> (HasSubset.Subset.{u2} (Finset.{u2} ι) (Finset.hasSubset.{u2} ι) s t) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) t v) r) (Finset.sum.{u1, u2} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) ι (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Insert.insert.{u2, u2} ι (Finset.{u2} ι) (Finset.hasInsert.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) i (SDiff.sdiff.{u2} (Finset.{u2} ι) (Finset.hasSdiff.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) t s)) v) r) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {t : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι t)) -> (Finset.Nonempty.{u2} ι s) -> (HasSubset.Subset.{u2} (Finset.{u2} ι) (Finset.instHasSubsetFinset.{u2} ι) s t) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) t v) r) (Finset.sum.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Insert.insert.{u2, u2} ι (Finset.{u2} ι) (Finset.instInsertFinset.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) i (SDiff.sdiff.{u2} (Finset.{u2} ι) (Finset.instSDiffFinset.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) t s)) v) r) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {t : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι t)) -> (Finset.Nonempty.{u2} ι s) -> (HasSubset.Subset.{u2} (Finset.{u2} ι) (Finset.instHasSubsetFinset.{u2} ι) s t) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) t v) r) (Finset.sum.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Insert.insert.{u2, u2} ι (Finset.{u2} ι) (Finset.instInsertFinset.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) i (SDiff.sdiff.{u2} (Finset.{u2} ι) (Finset.instSDiffFinset.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) t s)) v) r) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_sum_interpolate_insert_sdiff Lagrange.interpolate_eq_sum_interpolate_insert_sdiffₓ'. -/
 theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs : s.Nonempty)
     (hst : s ⊆ t) :
@@ -670,7 +670,7 @@ theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {j : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) j s) -> (Ne.{succ u2} ι i j) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHAdd.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.add'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s j) v) r) (Lagrange.basisDivisor.{u1} F _inst_1 (v i) (v j))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r) (Lagrange.basisDivisor.{u1} F _inst_1 (v j) (v i)))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {j : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) j s) -> (Ne.{succ u2} ι i j) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F 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(a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r) (Lagrange.basisDivisor.{u1} F _inst_1 (v j) (v i)))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {j : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) j s) -> (Ne.{succ u2} ι i j) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.add'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s j) v) r) (Lagrange.basisDivisor.{u1} F _inst_1 (v i) (v j))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r) (Lagrange.basisDivisor.{u1} F _inst_1 (v j) (v i)))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_add_interpolate_erase Lagrange.interpolate_eq_add_interpolate_eraseₓ'. -/
 theorem interpolate_eq_add_interpolate_erase (hvs : Set.InjOn v s) (hi : i ∈ s) (hj : j ∈ s)
     (hij : i ≠ j) :
@@ -821,7 +821,7 @@ theorem nodal_insert_eq_nodal (hi : i ∉ s) : nodal (insert i s) v = (X - C (v
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} [_inst_2 : DecidableEq.{succ u2} ι], Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} F F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.derivative.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)) (Finset.sum.{u1, u2} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) ι (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) s (fun (i : ι) => Lagrange.nodal.{u1, u2} F _inst_1 ι (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} {s : Finset.{u1} ι} {v : ι -> F} [_inst_2 : DecidableEq.{succ u1} ι], Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodal.{u2, u1} F _inst_1 ι s v)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (fun (_x : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} F F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Polynomial.derivative.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodal.{u2, u1} F _inst_1 ι s v)) (Finset.sum.{u2, u1} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) s (fun (i : ι) => Lagrange.nodal.{u2, u1} F _inst_1 ι (Finset.erase.{u1} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} {s : Finset.{u1} ι} {v : ι -> F} [_inst_2 : DecidableEq.{succ u1} ι], Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodal.{u2, u1} F _inst_1 ι s v)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (fun (_x : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} F F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Polynomial.derivative.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodal.{u2, u1} F _inst_1 ι s v)) (Finset.sum.{u2, u1} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) s (fun (i : ι) => Lagrange.nodal.{u2, u1} F _inst_1 ι (Finset.erase.{u1} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v))
 Case conversion may be inaccurate. Consider using '#align lagrange.derivative_nodal Lagrange.derivative_nodalₓ'. -/
 theorem derivative_nodal : (nodal s v).derivative = ∑ i in s, nodal (s.eraseₓ i) v :=
   by
@@ -838,7 +838,7 @@ theorem derivative_nodal : (nodal s v).derivative = ∑ i in s, nodal (s.erase
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u2} ι], (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} F F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.derivative.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v))) (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) (Lagrange.nodal.{u1, u2} F _inst_1 ι (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v)))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u2} ι], (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (v i) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} F F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Polynomial.derivative.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v))) (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (v i) (Lagrange.nodal.{u1, u2} F _inst_1 ι (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v)))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u2} ι], (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (v i) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} F F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Polynomial.derivative.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v))) (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (v i) (Lagrange.nodal.{u1, u2} F _inst_1 ι (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v)))
 Case conversion may be inaccurate. Consider using '#align lagrange.eval_nodal_derivative_eval_node_eq Lagrange.eval_nodal_derivative_eval_node_eqₓ'. -/
 theorem eval_nodal_derivative_eval_node_eq (hi : i ∈ s) :
     eval (v i) (nodal s v).derivative = eval (v i) (nodal (s.eraseₓ i) v) :=
@@ -871,7 +871,7 @@ theorem nodalWeight_eq_eval_nodal_erase_inv :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u2} ι], (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (DivInvMonoid.toHasInv.{u1} F (DivisionRing.toDivInvMonoid.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} F F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.derivative.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u2} ι], (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (v i) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} F F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Polynomial.derivative.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u2} ι], (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (v i) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} F F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Polynomial.derivative.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)))))
 Case conversion may be inaccurate. Consider using '#align lagrange.nodal_weight_eq_eval_nodal_derative Lagrange.nodalWeight_eq_eval_nodal_derativeₓ'. -/
 theorem nodalWeight_eq_eval_nodal_derative (hi : i ∈ s) :
     nodalWeight s v i = (eval (v i) (nodal s v).derivative)⁻¹ := by
@@ -921,7 +921,7 @@ theorem eval_basis_not_at_node (hi : i ∈ s) (hxi : x ≠ v i) :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) [_inst_2 : DecidableEq.{succ u2} ι], Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F 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(NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F 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(Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.hasDiv.{u1} F _inst_1)) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (v i))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (r i))))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) [_inst_2 : DecidableEq.{succ u1} ι], Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (Finset.sum.{u2, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (NonAssocRing.toNonUnitalNonAssocRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Ring.toNonAssocRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (CommRing.toRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (EuclideanDomain.toCommRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (HDiv.hDiv.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHDiv.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instDivPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1)) (Lagrange.nodal.{u2, u1} F _inst_1 ι s v) (HSub.hSub.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (v i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHSub.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.sub.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (Polynomial.X.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (v i))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i))))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) [_inst_2 : DecidableEq.{succ u1} ι], Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (Finset.sum.{u2, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (NonAssocRing.toNonUnitalNonAssocRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Ring.toNonAssocRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (CommRing.toRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (EuclideanDomain.toCommRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (HDiv.hDiv.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHDiv.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instDivPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1)) (Lagrange.nodal.{u2, u1} F _inst_1 ι s v) (HSub.hSub.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (v i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHSub.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.sub.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (Polynomial.X.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (v i))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_nodal_weight_mul_nodal_div_X_sub_C Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_Cₓ'. -/
 theorem interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C :
     interpolate s v r = ∑ i in s, C (nodalWeight s v i) * (nodal s v / (X - C (v i))) * C (r i) :=
@@ -932,7 +932,7 @@ theorem interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) x (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) x (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)) (Finset.sum.{u1, u2} F ι (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (DivInvMonoid.toHasInv.{u1} F (DivisionRing.toDivInvMonoid.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toHasSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (AddGroupWithOne.toAddGroup.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))) x (v i)))) (r i)))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))) (r i)))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))) (r i)))))
 Case conversion may be inaccurate. Consider using '#align lagrange.eval_interpolate_not_at_node Lagrange.eval_interpolate_not_at_nodeₓ'. -/
 /-- This is the first barycentric form of the Lagrange interpolant. -/
 theorem eval_interpolate_not_at_node (hx : ∀ i ∈ s, x ≠ v i) :
@@ -961,7 +961,7 @@ theorem sum_nodalWeight_mul_inv_sub_ne_zero (hvs : Set.InjOn v s) (hx : ∀ i 
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Finset.Nonempty.{u2} ι s) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) x (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HDiv.hDiv.{u1, u1, u1} F F F (instHDiv.{u1} F (DivInvMonoid.toHasDiv.{u1} F (DivisionRing.toDivInvMonoid.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Finset.sum.{u1, u2} F ι (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (DivInvMonoid.toHasInv.{u1} F (DivisionRing.toDivInvMonoid.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toHasSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (AddGroupWithOne.toAddGroup.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))) x (v i)))) (r i))) (Finset.sum.{u1, u2} F ι (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (DivInvMonoid.toHasInv.{u1} F (DivisionRing.toDivInvMonoid.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toHasSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (AddGroupWithOne.toAddGroup.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))) x (v i)))))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Finset.Nonempty.{u2} ι s) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HDiv.hDiv.{u1, u1, u1} F F F (instHDiv.{u1} F (Field.toDiv.{u1} F _inst_1)) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))) (r i))) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Finset.Nonempty.{u2} ι s) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HDiv.hDiv.{u1, u1, u1} F F F (instHDiv.{u1} F (Field.toDiv.{u1} F _inst_1)) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))) (r i))) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))))))
 Case conversion may be inaccurate. Consider using '#align lagrange.eval_interpolate_not_at_node' Lagrange.eval_interpolate_not_at_node'ₓ'. -/
 /-- This is the second barycentric form of the Lagrange interpolant. -/
 theorem eval_interpolate_not_at_node' (hvs : Set.InjOn v s) (hs : s.Nonempty)

b5ad1414

bump to nightly-2023-05-19-16

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

a31df521

Diff

@@ -441,7 +441,7 @@ theorem interpolate_empty : interpolate ∅ v r = 0 := by rw [interpolate_apply,
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {i : ι} {v : ι -> F} (r : ι -> F), Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Singleton.singleton.{u2, u2} ι (Finset.{u2} ι) (Finset.hasSingleton.{u2} ι) i) v) r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (r i))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {i : ι} {v : ι -> F} (r : ι -> F), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Singleton.singleton.{u1, u1} ι (Finset.{u1} ι) (Finset.instSingletonFinset.{u1} ι) i) v) r) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {i : ι} {v : ι -> F} (r : ι -> F), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Singleton.singleton.{u1, u1} ι (Finset.{u1} ι) (Finset.instSingletonFinset.{u1} ι) i) v) r) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_singleton Lagrange.interpolate_singletonₓ'. -/
 @[simp]
 theorem interpolate_singleton : interpolate {i} v r = C (r i) := by
@@ -712,7 +712,7 @@ def nodal (s : Finset ι) (v : ι → F) : F[X] :=
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} (s : Finset.{u2} ι) (v : ι -> F), Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v) (Finset.prod.{u1, u2} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.commRing.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)))) s (fun (i : ι) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (v i))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} (s : Finset.{u2} ι) (v : ι -> F), Eq.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v) (Finset.prod.{u1, u2} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.commRing.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)))) s (fun (i : ι) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i)) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} (s : Finset.{u2} ι) (v : ι -> F), Eq.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v) (Finset.prod.{u1, u2} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.commRing.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)))) s (fun (i : ι) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i)) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i))))
 Case conversion may be inaccurate. Consider using '#align lagrange.nodal_eq Lagrange.nodal_eqₓ'. -/
 theorem nodal_eq (s : Finset ι) (v : ι → F) : nodal s v = ∏ i in s, X - C (v i) :=
   rfl
@@ -777,7 +777,7 @@ theorem eval_nodal_not_at_node (hx : ∀ i ∈ s, x ≠ v i) : eval x (nodal s v
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u2} ι], (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (v i))) (Lagrange.nodal.{u1, u2} F _inst_1 ι (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v)))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u2} ι], (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i)) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i))) (Lagrange.nodal.{u1, u2} F _inst_1 ι (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v)))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u2} ι], (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i)) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i))) (Lagrange.nodal.{u1, u2} F _inst_1 ι (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v)))
 Case conversion may be inaccurate. Consider using '#align lagrange.nodal_eq_mul_nodal_erase Lagrange.nodal_eq_mul_nodal_eraseₓ'. -/
 theorem nodal_eq_mul_nodal_erase [DecidableEq ι] (hi : i ∈ s) :
     nodal s v = (X - C (v i)) * nodal (s.eraseₓ i) v := by simp_rw [nodal, mul_prod_erase _ _ hi]
@@ -787,7 +787,7 @@ theorem nodal_eq_mul_nodal_erase [DecidableEq ι] (hi : i ∈ s) :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {i : ι} (v : ι -> F), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Dvd.Dvd.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.commRing.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1))))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (v i))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {i : ι} (v : ι -> F), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Dvd.dvd.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.commRing.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1))))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i)) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {i : ι} (v : ι -> F), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Dvd.dvd.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.commRing.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1))))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i)) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v))
 Case conversion may be inaccurate. Consider using '#align lagrange.X_sub_C_dvd_nodal Lagrange.X_sub_C_dvd_nodalₓ'. -/
 theorem X_sub_C_dvd_nodal (v : ι → F) (hi : i ∈ s) : X - C (v i) ∣ nodal s v :=
   ⟨_, by classical exact nodal_eq_mul_nodal_erase hi⟩
@@ -799,7 +799,7 @@ variable [DecidableEq ι]
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u2} ι], (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.hasDiv.{u1} F _inst_1)) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (v i)))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u2} ι], (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instDivPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1)) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i)) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i)))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u2} ι], (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instDivPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1)) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i)) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i)))))
 Case conversion may be inaccurate. Consider using '#align lagrange.nodal_erase_eq_nodal_div Lagrange.nodal_erase_eq_nodal_divₓ'. -/
 theorem nodal_erase_eq_nodal_div (hi : i ∈ s) : nodal (s.eraseₓ i) v = nodal s v / (X - C (v i)) :=
   by
@@ -811,7 +811,7 @@ theorem nodal_erase_eq_nodal_div (hi : i ∈ s) : nodal (s.eraseₓ i) v = nodal
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u2} ι], (Not (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s)) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι (Insert.insert.{u2, u2} ι (Finset.{u2} ι) (Finset.hasInsert.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) i s) v) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (v i))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u2} ι], (Not (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s)) -> (Eq.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι (Insert.insert.{u2, u2} ι (Finset.{u2} ι) (Finset.instInsertFinset.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) i s) v) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i)) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u2} ι], (Not (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s)) -> (Eq.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι (Insert.insert.{u2, u2} ι (Finset.{u2} ι) (Finset.instInsertFinset.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) i s) v) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i)) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)))
 Case conversion may be inaccurate. Consider using '#align lagrange.nodal_insert_eq_nodal Lagrange.nodal_insert_eq_nodalₓ'. -/
 theorem nodal_insert_eq_nodal (hi : i ∉ s) : nodal (insert i s) v = (X - C (v i)) * nodal s v := by
   simp_rw [nodal, prod_insert hi]
@@ -896,7 +896,7 @@ theorem nodalWeight_ne_zero (hvs : Set.InjOn v s) (hi : i ∈ s) : nodalWeight s
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u2} ι], (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.hasDiv.{u1} F _inst_1)) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (v i))))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u2} ι], (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instDivPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1)) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i)) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i))))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u2} ι], (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instDivPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1)) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i)) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i))))))
 Case conversion may be inaccurate. Consider using '#align lagrange.basis_eq_prod_sub_inv_mul_nodal_div Lagrange.basis_eq_prod_sub_inv_mul_nodal_divₓ'. -/
 theorem basis_eq_prod_sub_inv_mul_nodal_div (hi : i ∈ s) :
     Lagrange.basis s v i = C (nodalWeight s v i) * (nodal s v / (X - C (v i))) := by
@@ -921,7 +921,7 @@ theorem eval_basis_not_at_node (hi : i ∈ s) (hxi : x ≠ v i) :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) [_inst_2 : DecidableEq.{succ u2} ι], Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (Finset.sum.{u1, u2} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) ι (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F 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(Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.hasDiv.{u1} F _inst_1)) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F 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(Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (v i))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F 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(RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (r i))))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) [_inst_2 : DecidableEq.{succ u1} ι], Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (Finset.sum.{u2, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (NonAssocRing.toNonUnitalNonAssocRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Ring.toNonAssocRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (CommRing.toRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (EuclideanDomain.toCommRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (HDiv.hDiv.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHDiv.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instDivPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1)) (Lagrange.nodal.{u2, u1} F _inst_1 ι s v) (HSub.hSub.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (v i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHSub.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.sub.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (Polynomial.X.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (v i))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i))))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) [_inst_2 : DecidableEq.{succ u1} ι], Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (Finset.sum.{u2, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (NonAssocRing.toNonUnitalNonAssocRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Ring.toNonAssocRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (CommRing.toRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (EuclideanDomain.toCommRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (HDiv.hDiv.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHDiv.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instDivPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1)) (Lagrange.nodal.{u2, u1} F _inst_1 ι s v) (HSub.hSub.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (v i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHSub.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.sub.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (Polynomial.X.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F 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F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (v i))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_nodal_weight_mul_nodal_div_X_sub_C Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_Cₓ'. -/
 theorem interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C :
     interpolate s v r = ∑ i in s, C (nodalWeight s v i) * (nodal s v / (X - C (v i))) * C (r i) :=

b5ad1414

bump to nightly-2023-05-18-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e

b46e9d53

Diff

@@ -431,7 +431,7 @@ def interpolate (s : Finset ι) (v : ι → F) : (ι → F) →ₗ[F] F[X]
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {v : ι -> F} (r : ι -> F), Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (EmptyCollection.emptyCollection.{u2} (Finset.{u2} ι) (Finset.hasEmptyc.{u2} ι)) v) r) (OfNat.ofNat.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.zero.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {v : ι -> F} (r : ι -> F), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (EmptyCollection.emptyCollection.{u1} (Finset.{u1} ι) (Finset.instEmptyCollectionFinset.{u1} ι)) v) r) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Polynomial.zero.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {v : ι -> F} (r : ι -> F), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (EmptyCollection.emptyCollection.{u1} (Finset.{u1} ι) (Finset.instEmptyCollectionFinset.{u1} ι)) v) r) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Polynomial.zero.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_empty Lagrange.interpolate_emptyₓ'. -/
 @[simp]
 theorem interpolate_empty : interpolate ∅ v r = 0 := by rw [interpolate_apply, sum_empty]
@@ -441,7 +441,7 @@ theorem interpolate_empty : interpolate ∅ v r = 0 := by rw [interpolate_apply,
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {i : ι} {v : ι -> F} (r : ι -> F), Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Singleton.singleton.{u2, u2} ι (Finset.{u2} ι) (Finset.hasSingleton.{u2} ι) i) v) r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (r i))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {i : ι} {v : ι -> F} (r : ι -> F), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Singleton.singleton.{u1, u1} ι (Finset.{u1} ι) (Finset.instSingletonFinset.{u1} ι) i) v) r) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {i : ι} {v : ι -> F} (r : ι -> F), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Singleton.singleton.{u1, u1} ι (Finset.{u1} ι) (Finset.instSingletonFinset.{u1} ι) i) v) r) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_singleton Lagrange.interpolate_singletonₓ'. -/
 @[simp]
 theorem interpolate_singleton : interpolate {i} v r = C (r i) := by
@@ -452,7 +452,7 @@ theorem interpolate_singleton : interpolate {i} v r = C (r i) := by
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F}, (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Finset.Nonempty.{u2} ι s) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (OfNat.ofNat.{max u2 u1} (ι -> F) 1 (OfNat.mk.{max u2 u1} (ι -> F) 1 (One.one.{max u2 u1} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddMonoidWithOne.toOne.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) (OfNat.ofNat.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 1 (OfNat.mk.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 1 (One.one.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.hasOne.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F}, (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Finset.Nonempty.{u2} ι s) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Polynomial.one.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F}, (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Finset.Nonempty.{u2} ι s) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Polynomial.one.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_one Lagrange.interpolate_oneₓ'. -/
 theorem interpolate_one (hvs : Set.InjOn v s) (hs : s.Nonempty) : interpolate s v 1 = 1 :=
   by
@@ -464,7 +464,7 @@ theorem interpolate_one (hvs : Set.InjOn v s) (hs : s.Nonempty) : interpolate s
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (r i))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (v i) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (r i))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (v i) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (r i))
 Case conversion may be inaccurate. Consider using '#align lagrange.eval_interpolate_at_node Lagrange.eval_interpolate_at_nodeₓ'. -/
 theorem eval_interpolate_at_node (hvs : Set.InjOn v s) (hi : i ∈ s) :
     eval (v i) (interpolate s v r) = r i :=
@@ -479,7 +479,7 @@ theorem eval_interpolate_at_node (hvs : Set.InjOn v s) (hi : i ∈ s) :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toHasLe.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
 Case conversion may be inaccurate. Consider using '#align lagrange.degree_interpolate_le Lagrange.degree_interpolate_leₓ'. -/
 theorem degree_interpolate_le (hvs : Set.InjOn v s) : (interpolate s v r).degree ≤ ↑(s.card - 1) :=
   by
@@ -496,7 +496,7 @@ theorem degree_interpolate_le (hvs : Set.InjOn v s) : (interpolate s v r).degree
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s)))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u2} ι s)))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u2} ι s)))
 Case conversion may be inaccurate. Consider using '#align lagrange.degree_interpolate_lt Lagrange.degree_interpolate_ltₓ'. -/
 theorem degree_interpolate_lt (hvs : Set.InjOn v s) : (interpolate s v r).degree < s.card :=
   by
@@ -512,7 +512,7 @@ theorem degree_interpolate_lt (hvs : Set.InjOn v s) : (interpolate s v r).degree
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
 Case conversion may be inaccurate. Consider using '#align lagrange.degree_interpolate_erase_lt Lagrange.degree_interpolate_erase_ltₓ'. -/
 theorem degree_interpolate_erase_lt (hvs : Set.InjOn v s) (hi : i ∈ s) :
     (interpolate (s.eraseₓ i) v r).degree < ↑(s.card - 1) :=
@@ -525,7 +525,7 @@ theorem degree_interpolate_erase_lt (hvs : Set.InjOn v s) (hi : i ∈ s) :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F 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(DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i)))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i)))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i)))
 Case conversion may be inaccurate. Consider using '#align lagrange.values_eq_on_of_interpolate_eq Lagrange.values_eq_on_of_interpolate_eqₓ'. -/
 theorem values_eq_on_of_interpolate_eq (hvs : Set.InjOn v s)
     (hrr' : interpolate s v r = interpolate s v r') : ∀ i ∈ s, r i = r' i := fun _ hi => by
@@ -536,7 +536,7 @@ theorem values_eq_on_of_interpolate_eq (hvs : Set.InjOn v s)
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r'))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r'))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r'))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_of_values_eq_on Lagrange.interpolate_eq_of_values_eq_onₓ'. -/
 theorem interpolate_eq_of_values_eq_on (hrr' : ∀ i ∈ s, r i = r' i) :
     interpolate s v r = interpolate s v r' :=
@@ -547,7 +547,7 @@ theorem interpolate_eq_of_values_eq_on (hrr' : ∀ i ∈ s, r i = r' i) :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Iff (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} 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(Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F 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(Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_iff_values_eq_on Lagrange.interpolate_eq_iff_values_eq_onₓ'. -/
 theorem interpolate_eq_iff_values_eq_on (hvs : Set.InjOn v s) :
     interpolate s v r = interpolate s v r' ↔ ∀ i ∈ s, r i = r' i :=
@@ -558,7 +558,7 @@ theorem interpolate_eq_iff_values_eq_on (hvs : Set.InjOn v s) :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s))) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (fun (i : ι) => Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) f)))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) -> (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (fun (i : ι) => Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f)))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) -> (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (fun (i : ι) => Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f)))
 Case conversion may be inaccurate. Consider using '#align lagrange.eq_interpolate Lagrange.eq_interpolateₓ'. -/
 theorem eq_interpolate {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree < s.card) :
     f = interpolate s v fun i => f.eval (v i) :=
@@ -570,7 +570,7 @@ theorem eq_interpolate {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s))) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) f) (r i))) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u2} F (Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f) (r i))) -> (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u2} F (Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f) (r i))) -> (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r))
 Case conversion may be inaccurate. Consider using '#align lagrange.eq_interpolate_of_eval_eq Lagrange.eq_interpolate_of_eval_eqₓ'. -/
 theorem eq_interpolate_of_eval_eq {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree < s.card)
     (eval_f : ∀ i ∈ s, f.eval (v i) = r i) : f = interpolate s v r :=
@@ -583,7 +583,7 @@ theorem eq_interpolate_of_eval_eq {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Iff (And (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s))) (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) f) (r i)))) (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (Iff (And (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u2} F (Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f) (r i)))) (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (Iff (And (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u2} F (Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f) (r i)))) (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)))
 Case conversion may be inaccurate. Consider using '#align lagrange.eq_interpolate_iff Lagrange.eq_interpolate_iffₓ'. -/
 /-- This is the characteristic property of the interpolation: the interpolation is the
 unique polynomial of `degree < fintype.card ι` which takes the value of the `r i` on the `v i`.
@@ -626,7 +626,7 @@ def funEquivDegreeLT (hvs : Set.InjOn v s) : degreeLT F s.card ≃ₗ[F] s → F
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {t : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) t)) -> (Finset.Nonempty.{u2} ι s) -> (HasSubset.Subset.{u2} (Finset.{u2} ι) (Finset.hasSubset.{u2} ι) s t) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) t v) r) (Finset.sum.{u1, u2} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) ι (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Insert.insert.{u2, u2} ι (Finset.{u2} ι) (Finset.hasInsert.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) i (SDiff.sdiff.{u2} (Finset.{u2} ι) (Finset.hasSdiff.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) t s)) v) r) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {t : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι t)) -> (Finset.Nonempty.{u2} ι s) -> (HasSubset.Subset.{u2} (Finset.{u2} ι) (Finset.instHasSubsetFinset.{u2} ι) s t) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) t v) r) (Finset.sum.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Insert.insert.{u2, u2} ι (Finset.{u2} ι) (Finset.instInsertFinset.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) i (SDiff.sdiff.{u2} (Finset.{u2} ι) (Finset.instSDiffFinset.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) t s)) v) r) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {t : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι t)) -> (Finset.Nonempty.{u2} ι s) -> (HasSubset.Subset.{u2} (Finset.{u2} ι) (Finset.instHasSubsetFinset.{u2} ι) s t) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) t v) r) (Finset.sum.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Insert.insert.{u2, u2} ι (Finset.{u2} ι) (Finset.instInsertFinset.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) i (SDiff.sdiff.{u2} (Finset.{u2} ι) (Finset.instSDiffFinset.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) t s)) v) r) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_sum_interpolate_insert_sdiff Lagrange.interpolate_eq_sum_interpolate_insert_sdiffₓ'. -/
 theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs : s.Nonempty)
     (hst : s ⊆ t) :
@@ -670,7 +670,7 @@ theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {j : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) j s) -> (Ne.{succ u2} ι i j) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHAdd.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.add'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s j) v) r) (Lagrange.basisDivisor.{u1} F _inst_1 (v i) (v j))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r) (Lagrange.basisDivisor.{u1} F _inst_1 (v j) (v i)))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {j : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) j s) -> (Ne.{succ u2} ι i j) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F 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(a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r) (Lagrange.basisDivisor.{u1} F _inst_1 (v j) (v i)))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {j : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) j s) -> (Ne.{succ u2} ι i j) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.add'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s j) v) r) (Lagrange.basisDivisor.{u1} F _inst_1 (v i) (v j))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r) (Lagrange.basisDivisor.{u1} F _inst_1 (v j) (v i)))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_add_interpolate_erase Lagrange.interpolate_eq_add_interpolate_eraseₓ'. -/
 theorem interpolate_eq_add_interpolate_erase (hvs : Set.InjOn v s) (hi : i ∈ s) (hj : j ∈ s)
     (hij : i ≠ j) :
@@ -821,7 +821,7 @@ theorem nodal_insert_eq_nodal (hi : i ∉ s) : nodal (insert i s) v = (X - C (v
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} [_inst_2 : DecidableEq.{succ u2} ι], Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} F F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.derivative.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)) (Finset.sum.{u1, u2} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) ι (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) s (fun (i : ι) => Lagrange.nodal.{u1, u2} F _inst_1 ι (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} {s : Finset.{u1} ι} {v : ι -> F} [_inst_2 : DecidableEq.{succ u1} ι], Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodal.{u2, u1} F _inst_1 ι s v)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (fun (_x : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} F F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Polynomial.derivative.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodal.{u2, u1} F _inst_1 ι s v)) (Finset.sum.{u2, u1} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) s (fun (i : ι) => Lagrange.nodal.{u2, u1} F _inst_1 ι (Finset.erase.{u1} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} {s : Finset.{u1} ι} {v : ι -> F} [_inst_2 : DecidableEq.{succ u1} ι], Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodal.{u2, u1} F _inst_1 ι s v)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (fun (_x : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} F F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Polynomial.derivative.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodal.{u2, u1} F _inst_1 ι s v)) (Finset.sum.{u2, u1} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) s (fun (i : ι) => Lagrange.nodal.{u2, u1} F _inst_1 ι (Finset.erase.{u1} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v))
 Case conversion may be inaccurate. Consider using '#align lagrange.derivative_nodal Lagrange.derivative_nodalₓ'. -/
 theorem derivative_nodal : (nodal s v).derivative = ∑ i in s, nodal (s.eraseₓ i) v :=
   by
@@ -838,7 +838,7 @@ theorem derivative_nodal : (nodal s v).derivative = ∑ i in s, nodal (s.erase
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u2} ι], (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} F F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.derivative.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v))) (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) (Lagrange.nodal.{u1, u2} F _inst_1 ι (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v)))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u2} ι], (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (v i) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} F F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Polynomial.derivative.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v))) (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (v i) (Lagrange.nodal.{u1, u2} F _inst_1 ι (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v)))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u2} ι], (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (v i) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} F F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Polynomial.derivative.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v))) (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (v i) (Lagrange.nodal.{u1, u2} F _inst_1 ι (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v)))
 Case conversion may be inaccurate. Consider using '#align lagrange.eval_nodal_derivative_eval_node_eq Lagrange.eval_nodal_derivative_eval_node_eqₓ'. -/
 theorem eval_nodal_derivative_eval_node_eq (hi : i ∈ s) :
     eval (v i) (nodal s v).derivative = eval (v i) (nodal (s.eraseₓ i) v) :=
@@ -871,7 +871,7 @@ theorem nodalWeight_eq_eval_nodal_erase_inv :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u2} ι], (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (DivInvMonoid.toHasInv.{u1} F (DivisionRing.toDivInvMonoid.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} F F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.derivative.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u2} ι], (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (v i) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} F F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Polynomial.derivative.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u2} ι], (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (v i) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} F F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Polynomial.derivative.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)))))
 Case conversion may be inaccurate. Consider using '#align lagrange.nodal_weight_eq_eval_nodal_derative Lagrange.nodalWeight_eq_eval_nodal_derativeₓ'. -/
 theorem nodalWeight_eq_eval_nodal_derative (hi : i ∈ s) :
     nodalWeight s v i = (eval (v i) (nodal s v).derivative)⁻¹ := by
@@ -921,7 +921,7 @@ theorem eval_basis_not_at_node (hi : i ∈ s) (hxi : x ≠ v i) :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) [_inst_2 : DecidableEq.{succ u2} ι], Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F 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(NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F 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(Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.hasDiv.{u1} F _inst_1)) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (v i))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (r i))))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) [_inst_2 : DecidableEq.{succ u1} ι], Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (Finset.sum.{u2, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (NonAssocRing.toNonUnitalNonAssocRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Ring.toNonAssocRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (CommRing.toRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (EuclideanDomain.toCommRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (HDiv.hDiv.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHDiv.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instDivPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1)) (Lagrange.nodal.{u2, u1} F _inst_1 ι s v) (HSub.hSub.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (v i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHSub.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.sub.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (Polynomial.X.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (v i))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i))))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) [_inst_2 : DecidableEq.{succ u1} ι], Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (Finset.sum.{u2, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (NonAssocRing.toNonUnitalNonAssocRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Ring.toNonAssocRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (CommRing.toRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (EuclideanDomain.toCommRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (HDiv.hDiv.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHDiv.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instDivPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1)) (Lagrange.nodal.{u2, u1} F _inst_1 ι s v) (HSub.hSub.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (v i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHSub.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.sub.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (Polynomial.X.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (v i))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_nodal_weight_mul_nodal_div_X_sub_C Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_Cₓ'. -/
 theorem interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C :
     interpolate s v r = ∑ i in s, C (nodalWeight s v i) * (nodal s v / (X - C (v i))) * C (r i) :=
@@ -932,7 +932,7 @@ theorem interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) x (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) x (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)) (Finset.sum.{u1, u2} F ι (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (DivInvMonoid.toHasInv.{u1} F (DivisionRing.toDivInvMonoid.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toHasSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (AddGroupWithOne.toAddGroup.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))) x (v i)))) (r i)))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))) (r i)))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))) (r i)))))
 Case conversion may be inaccurate. Consider using '#align lagrange.eval_interpolate_not_at_node Lagrange.eval_interpolate_not_at_nodeₓ'. -/
 /-- This is the first barycentric form of the Lagrange interpolant. -/
 theorem eval_interpolate_not_at_node (hx : ∀ i ∈ s, x ≠ v i) :
@@ -961,7 +961,7 @@ theorem sum_nodalWeight_mul_inv_sub_ne_zero (hvs : Set.InjOn v s) (hx : ∀ i 
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Finset.Nonempty.{u2} ι s) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) x (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HDiv.hDiv.{u1, u1, u1} F F F (instHDiv.{u1} F (DivInvMonoid.toHasDiv.{u1} F (DivisionRing.toDivInvMonoid.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Finset.sum.{u1, u2} F ι (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (DivInvMonoid.toHasInv.{u1} F (DivisionRing.toDivInvMonoid.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toHasSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (AddGroupWithOne.toAddGroup.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))) x (v i)))) (r i))) (Finset.sum.{u1, u2} F ι (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (DivInvMonoid.toHasInv.{u1} F (DivisionRing.toDivInvMonoid.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toHasSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (AddGroupWithOne.toAddGroup.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))) x (v i)))))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Finset.Nonempty.{u2} ι s) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HDiv.hDiv.{u1, u1, u1} F F F (instHDiv.{u1} F (Field.toDiv.{u1} F _inst_1)) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))) (r i))) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Finset.Nonempty.{u2} ι s) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HDiv.hDiv.{u1, u1, u1} F F F (instHDiv.{u1} F (Field.toDiv.{u1} F _inst_1)) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))) (r i))) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))))))
 Case conversion may be inaccurate. Consider using '#align lagrange.eval_interpolate_not_at_node' Lagrange.eval_interpolate_not_at_node'ₓ'. -/
 /-- This is the second barycentric form of the Lagrange interpolant. -/
 theorem eval_interpolate_not_at_node' (hvs : Set.InjOn v s) (hs : s.Nonempty)

b5ad1414

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -53,7 +53,7 @@ variable (s : Finset R)
 
 /- warning: polynomial.eq_zero_of_degree_lt_of_eval_finset_eq_zero -> Polynomial.eq_zero_of_degree_lt_of_eval_finset_eq_zero is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} (s : Finset.{u1} R), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u1} R s))) -> (forall (x : R), (Membership.Mem.{u1, u1} R (Finset.{u1} R) (Finset.hasMem.{u1} R) x s) -> (Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x f) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} (s : Finset.{u1} R), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u1} R s))) -> (forall (x : R), (Membership.Mem.{u1, u1} R (Finset.{u1} R) (Finset.hasMem.{u1} R) x s) -> (Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x f) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} (s : Finset.{u1} R), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} R s))) -> (forall (x : R), (Membership.mem.{u1, u1} R (Finset.{u1} R) (Finset.instMembershipFinset.{u1} R) x s) -> (Eq.{succ u1} R (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) x f) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) f (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eq_zero_of_degree_lt_of_eval_finset_eq_zero Polynomial.eq_zero_of_degree_lt_of_eval_finset_eq_zeroₓ'. -/
@@ -69,7 +69,12 @@ theorem eq_zero_of_degree_lt_of_eval_finset_eq_zero (degree_f_lt : f.degree < s.
       fun _ => eval_f _ (Finset.coe_mem _)
 #align polynomial.eq_zero_of_degree_lt_of_eval_finset_eq_zero Polynomial.eq_zero_of_degree_lt_of_eval_finset_eq_zero
 
-#print Polynomial.eq_of_degree_sub_lt_of_eval_finset_eq /-
+/- warning: polynomial.eq_of_degree_sub_lt_of_eval_finset_eq -> Polynomial.eq_of_degree_sub_lt_of_eval_finset_eq is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {g : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} (s : Finset.{u1} R), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) f g)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u1} R s))) -> (forall (x : R), (Membership.Mem.{u1, u1} R (Finset.{u1} R) (Finset.hasMem.{u1} R) x s) -> (Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x f) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x g))) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f g)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {g : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} (s : Finset.{u1} R), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) f g)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} R s))) -> (forall (x : R), (Membership.mem.{u1, u1} R (Finset.{u1} R) (Finset.instMembershipFinset.{u1} R) x s) -> (Eq.{succ u1} R (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) x f) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) x g))) -> (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) f g)
+Case conversion may be inaccurate. Consider using '#align polynomial.eq_of_degree_sub_lt_of_eval_finset_eq Polynomial.eq_of_degree_sub_lt_of_eval_finset_eqₓ'. -/
 theorem eq_of_degree_sub_lt_of_eval_finset_eq (degree_fg_lt : (f - g).degree < s.card)
     (eval_fg : ∀ x ∈ s, f.eval x = g.eval x) : f = g :=
   by
@@ -78,9 +83,13 @@ theorem eq_of_degree_sub_lt_of_eval_finset_eq (degree_fg_lt : (f - g).degree < s
   simp_rw [eval_sub, sub_eq_zero]
   exact eval_fg
 #align polynomial.eq_of_degree_sub_lt_of_eval_finset_eq Polynomial.eq_of_degree_sub_lt_of_eval_finset_eq
--/
 
-#print Polynomial.eq_of_degrees_lt_of_eval_finset_eq /-
+/- warning: polynomial.eq_of_degrees_lt_of_eval_finset_eq -> Polynomial.eq_of_degrees_lt_of_eval_finset_eq is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {g : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} (s : Finset.{u1} R), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u1} R s))) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) g) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u1} R s))) -> (forall (x : R), (Membership.Mem.{u1, u1} R (Finset.{u1} R) (Finset.hasMem.{u1} R) x s) -> (Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x f) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x g))) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f g)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {g : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} (s : Finset.{u1} R), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} R s))) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) g) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} R s))) -> (forall (x : R), (Membership.mem.{u1, u1} R (Finset.{u1} R) (Finset.instMembershipFinset.{u1} R) x s) -> (Eq.{succ u1} R (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) x f) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) x g))) -> (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) f g)
+Case conversion may be inaccurate. Consider using '#align polynomial.eq_of_degrees_lt_of_eval_finset_eq Polynomial.eq_of_degrees_lt_of_eval_finset_eqₓ'. -/
 theorem eq_of_degrees_lt_of_eval_finset_eq (degree_f_lt : f.degree < s.card)
     (degree_g_lt : g.degree < s.card) (eval_fg : ∀ x ∈ s, f.eval x = g.eval x) : f = g :=
   by
@@ -88,7 +97,6 @@ theorem eq_of_degrees_lt_of_eval_finset_eq (degree_f_lt : f.degree < s.card)
   refine' eq_of_degree_sub_lt_of_eval_finset_eq _ _ eval_fg
   rw [← mem_degree_lt]; exact Submodule.sub_mem _ degree_f_lt degree_g_lt
 #align polynomial.eq_of_degrees_lt_of_eval_finset_eq Polynomial.eq_of_degrees_lt_of_eval_finset_eq
--/
 
 end Finset
 
@@ -100,7 +108,7 @@ variable {ι : Type _} {v : ι → R} (s : Finset ι)
 
 /- warning: polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zero -> Polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zero is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {ι : Type.{u2}} {v : ι -> R} (s : Finset.{u2} ι), (Set.InjOn.{u2, u1} ι R v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s))) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (v i) f) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {ι : Type.{u2}} {v : ι -> R} (s : Finset.{u2} ι), (Set.InjOn.{u2, u1} ι R v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s))) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (v i) f) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {ι : Type.{u2}} {v : ι -> R} (s : Finset.{u2} ι), (Set.InjOn.{u2, u1} ι R v (Finset.toSet.{u2} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u2} ι s))) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} R (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (v i) f) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) f (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zero Polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zeroₓ'. -/
@@ -114,7 +122,12 @@ theorem eq_zero_of_degree_lt_of_eval_index_eq_zero (hvs : Set.InjOn v s)
     exact eval_f _ hj
 #align polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zero Polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zero
 
-#print Polynomial.eq_of_degree_sub_lt_of_eval_index_eq /-
+/- warning: polynomial.eq_of_degree_sub_lt_of_eval_index_eq -> Polynomial.eq_of_degree_sub_lt_of_eval_index_eq is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {g : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {ι : Type.{u2}} {v : ι -> R} (s : Finset.{u2} ι), (Set.InjOn.{u2, u1} ι R v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) f g)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s))) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (v i) f) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (v i) g))) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f g)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {g : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {ι : Type.{u2}} {v : ι -> R} (s : Finset.{u2} ι), (Set.InjOn.{u2, u1} ι R v (Finset.toSet.{u2} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) f g)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u2} ι s))) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} R (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (v i) f) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (v i) g))) -> (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) f g)
+Case conversion may be inaccurate. Consider using '#align polynomial.eq_of_degree_sub_lt_of_eval_index_eq Polynomial.eq_of_degree_sub_lt_of_eval_index_eqₓ'. -/
 theorem eq_of_degree_sub_lt_of_eval_index_eq (hvs : Set.InjOn v s)
     (degree_fg_lt : (f - g).degree < s.card) (eval_fg : ∀ i ∈ s, f.eval (v i) = g.eval (v i)) :
     f = g := by
@@ -123,9 +136,13 @@ theorem eq_of_degree_sub_lt_of_eval_index_eq (hvs : Set.InjOn v s)
   simp_rw [eval_sub, sub_eq_zero]
   exact eval_fg
 #align polynomial.eq_of_degree_sub_lt_of_eval_index_eq Polynomial.eq_of_degree_sub_lt_of_eval_index_eq
--/
 
-#print Polynomial.eq_of_degrees_lt_of_eval_index_eq /-
+/- warning: polynomial.eq_of_degrees_lt_of_eval_index_eq -> Polynomial.eq_of_degrees_lt_of_eval_index_eq is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {g : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {ι : Type.{u2}} {v : ι -> R} (s : Finset.{u2} ι), (Set.InjOn.{u2, u1} ι R v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s))) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) g) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s))) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (v i) f) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (v i) g))) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f g)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {g : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {ι : Type.{u2}} {v : ι -> R} (s : Finset.{u2} ι), (Set.InjOn.{u2, u1} ι R v (Finset.toSet.{u2} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u2} ι s))) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) g) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u2} ι s))) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} R (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (v i) f) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (v i) g))) -> (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) f g)
+Case conversion may be inaccurate. Consider using '#align polynomial.eq_of_degrees_lt_of_eval_index_eq Polynomial.eq_of_degrees_lt_of_eval_index_eqₓ'. -/
 theorem eq_of_degrees_lt_of_eval_index_eq (hvs : Set.InjOn v s) (degree_f_lt : f.degree < s.card)
     (degree_g_lt : g.degree < s.card) (eval_fg : ∀ i ∈ s, f.eval (v i) = g.eval (v i)) : f = g :=
   by
@@ -133,7 +150,6 @@ theorem eq_of_degrees_lt_of_eval_index_eq (hvs : Set.InjOn v s) (degree_f_lt : f
   rw [← mem_degree_lt] at degree_f_lt degree_g_lt⊢
   exact Submodule.sub_mem _ degree_f_lt degree_g_lt
 #align polynomial.eq_of_degrees_lt_of_eval_index_eq Polynomial.eq_of_degrees_lt_of_eval_index_eq
--/
 
 end Indexed
 
@@ -461,7 +477,7 @@ theorem eval_interpolate_at_node (hvs : Set.InjOn v s) (hi : i ∈ s) :
 
 /- warning: lagrange.degree_interpolate_le -> Lagrange.degree_interpolate_le is a dubious translation:
 lean 3 declaration is
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toHasLe.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))
 but is expected to have type
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
 Case conversion may be inaccurate. Consider using '#align lagrange.degree_interpolate_le Lagrange.degree_interpolate_leₓ'. -/
@@ -478,7 +494,7 @@ theorem degree_interpolate_le (hvs : Set.InjOn v s) : (interpolate s v r).degree
 
 /- warning: lagrange.degree_interpolate_lt -> Lagrange.degree_interpolate_lt is a dubious translation:
 lean 3 declaration is
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s)))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s)))
 but is expected to have type
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u2} ι s)))
 Case conversion may be inaccurate. Consider using '#align lagrange.degree_interpolate_lt Lagrange.degree_interpolate_ltₓ'. -/
@@ -494,7 +510,7 @@ theorem degree_interpolate_lt (hvs : Set.InjOn v s) : (interpolate s v r).degree
 
 /- warning: lagrange.degree_interpolate_erase_lt -> Lagrange.degree_interpolate_erase_lt is a dubious translation:
 lean 3 declaration is
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} 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(Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))
 but is expected to have type
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
 Case conversion may be inaccurate. Consider using '#align lagrange.degree_interpolate_erase_lt Lagrange.degree_interpolate_erase_ltₓ'. -/
@@ -540,7 +556,7 @@ theorem interpolate_eq_iff_values_eq_on (hvs : Set.InjOn v s) :
 
 /- warning: lagrange.eq_interpolate -> Lagrange.eq_interpolate is a dubious translation:
 lean 3 declaration is
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s))) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (fun (i : ι) => Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) f)))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s))) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (fun (i : ι) => Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) f)))
 but is expected to have type
   forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) -> (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (fun (i : ι) => Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f)))
 Case conversion may be inaccurate. Consider using '#align lagrange.eq_interpolate Lagrange.eq_interpolateₓ'. -/
@@ -552,7 +568,7 @@ theorem eq_interpolate {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree
 
 /- warning: lagrange.eq_interpolate_of_eval_eq -> Lagrange.eq_interpolate_of_eval_eq is a dubious translation:
 lean 3 declaration is
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s))) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) f) (r i))) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F 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(Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s))) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) f) (r i))) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F 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(Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r))
 but is expected to have type
   forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u2} F (Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f) (r i))) -> (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r))
 Case conversion may be inaccurate. Consider using '#align lagrange.eq_interpolate_of_eval_eq Lagrange.eq_interpolate_of_eval_eqₓ'. -/
@@ -565,7 +581,7 @@ theorem eq_interpolate_of_eval_eq {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt
 
 /- warning: lagrange.eq_interpolate_iff -> Lagrange.eq_interpolate_iff is a dubious translation:
 lean 3 declaration is
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Iff (And (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s))) (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) f) (r i)))) (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Iff (And (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s))) (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) f) (r i)))) (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)))
 but is expected to have type
   forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (Iff (And (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u2} F (Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f) (r i)))) (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)))
 Case conversion may be inaccurate. Consider using '#align lagrange.eq_interpolate_iff Lagrange.eq_interpolate_iffₓ'. -/

b5ad1414

bump to nightly-2023-05-16-14

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

b356e20f

Diff

@@ -415,7 +415,7 @@ def interpolate (s : Finset ι) (v : ι → F) : (ι → F) →ₗ[F] F[X]
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {v : ι -> F} (r : ι -> F), Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (EmptyCollection.emptyCollection.{u2} (Finset.{u2} ι) (Finset.hasEmptyc.{u2} ι)) v) r) (OfNat.ofNat.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.zero.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {v : ι -> F} (r : ι -> F), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (EmptyCollection.emptyCollection.{u1} (Finset.{u1} ι) (Finset.instEmptyCollectionFinset.{u1} ι)) v) r) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Polynomial.zero.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {v : ι -> F} (r : ι -> F), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (EmptyCollection.emptyCollection.{u1} (Finset.{u1} ι) (Finset.instEmptyCollectionFinset.{u1} ι)) v) r) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Polynomial.zero.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_empty Lagrange.interpolate_emptyₓ'. -/
 @[simp]
 theorem interpolate_empty : interpolate ∅ v r = 0 := by rw [interpolate_apply, sum_empty]
@@ -425,7 +425,7 @@ theorem interpolate_empty : interpolate ∅ v r = 0 := by rw [interpolate_apply,
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {i : ι} {v : ι -> F} (r : ι -> F), Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Singleton.singleton.{u2, u2} ι (Finset.{u2} ι) (Finset.hasSingleton.{u2} ι) i) v) r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (r i))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {i : ι} {v : ι -> F} (r : ι -> F), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Singleton.singleton.{u1, u1} ι (Finset.{u1} ι) (Finset.instSingletonFinset.{u1} ι) i) v) r) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {i : ι} {v : ι -> F} (r : ι -> F), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Singleton.singleton.{u1, u1} ι (Finset.{u1} ι) (Finset.instSingletonFinset.{u1} ι) i) v) r) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_singleton Lagrange.interpolate_singletonₓ'. -/
 @[simp]
 theorem interpolate_singleton : interpolate {i} v r = C (r i) := by
@@ -436,7 +436,7 @@ theorem interpolate_singleton : interpolate {i} v r = C (r i) := by
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F}, (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Finset.Nonempty.{u2} ι s) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (OfNat.ofNat.{max u2 u1} (ι -> F) 1 (OfNat.mk.{max u2 u1} (ι -> F) 1 (One.one.{max u2 u1} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddMonoidWithOne.toOne.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) (OfNat.ofNat.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 1 (OfNat.mk.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 1 (One.one.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.hasOne.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F}, (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Finset.Nonempty.{u2} ι s) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Polynomial.one.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F}, (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Finset.Nonempty.{u2} ι s) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Polynomial.one.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_one Lagrange.interpolate_oneₓ'. -/
 theorem interpolate_one (hvs : Set.InjOn v s) (hs : s.Nonempty) : interpolate s v 1 = 1 :=
   by
@@ -448,7 +448,7 @@ theorem interpolate_one (hvs : Set.InjOn v s) (hs : s.Nonempty) : interpolate s
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (r i))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (v i) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (r i))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (v i) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (r i))
 Case conversion may be inaccurate. Consider using '#align lagrange.eval_interpolate_at_node Lagrange.eval_interpolate_at_nodeₓ'. -/
 theorem eval_interpolate_at_node (hvs : Set.InjOn v s) (hi : i ∈ s) :
     eval (v i) (interpolate s v r) = r i :=
@@ -463,7 +463,7 @@ theorem eval_interpolate_at_node (hvs : Set.InjOn v s) (hi : i ∈ s) :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
 Case conversion may be inaccurate. Consider using '#align lagrange.degree_interpolate_le Lagrange.degree_interpolate_leₓ'. -/
 theorem degree_interpolate_le (hvs : Set.InjOn v s) : (interpolate s v r).degree ≤ ↑(s.card - 1) :=
   by
@@ -480,7 +480,7 @@ theorem degree_interpolate_le (hvs : Set.InjOn v s) : (interpolate s v r).degree
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s)))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u2} ι s)))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u2} ι s)))
 Case conversion may be inaccurate. Consider using '#align lagrange.degree_interpolate_lt Lagrange.degree_interpolate_ltₓ'. -/
 theorem degree_interpolate_lt (hvs : Set.InjOn v s) : (interpolate s v r).degree < s.card :=
   by
@@ -496,7 +496,7 @@ theorem degree_interpolate_lt (hvs : Set.InjOn v s) : (interpolate s v r).degree
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
 Case conversion may be inaccurate. Consider using '#align lagrange.degree_interpolate_erase_lt Lagrange.degree_interpolate_erase_ltₓ'. -/
 theorem degree_interpolate_erase_lt (hvs : Set.InjOn v s) (hi : i ∈ s) :
     (interpolate (s.eraseₓ i) v r).degree < ↑(s.card - 1) :=
@@ -509,7 +509,7 @@ theorem degree_interpolate_erase_lt (hvs : Set.InjOn v s) (hi : i ∈ s) :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F 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(DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i)))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i)))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i)))
 Case conversion may be inaccurate. Consider using '#align lagrange.values_eq_on_of_interpolate_eq Lagrange.values_eq_on_of_interpolate_eqₓ'. -/
 theorem values_eq_on_of_interpolate_eq (hvs : Set.InjOn v s)
     (hrr' : interpolate s v r = interpolate s v r') : ∀ i ∈ s, r i = r' i := fun _ hi => by
@@ -520,7 +520,7 @@ theorem values_eq_on_of_interpolate_eq (hvs : Set.InjOn v s)
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F 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(DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F 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 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F 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(Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r'))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} 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(Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r'))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_of_values_eq_on Lagrange.interpolate_eq_of_values_eq_onₓ'. -/
 theorem interpolate_eq_of_values_eq_on (hrr' : ∀ i ∈ s, r i = r' i) :
     interpolate s v r = interpolate s v r' :=
@@ -531,7 +531,7 @@ theorem interpolate_eq_of_values_eq_on (hrr' : ∀ i ∈ s, r i = r' i) :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Iff (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} 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(Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_iff_values_eq_on Lagrange.interpolate_eq_iff_values_eq_onₓ'. -/
 theorem interpolate_eq_iff_values_eq_on (hvs : Set.InjOn v s) :
     interpolate s v r = interpolate s v r' ↔ ∀ i ∈ s, r i = r' i :=
@@ -542,7 +542,7 @@ theorem interpolate_eq_iff_values_eq_on (hvs : Set.InjOn v s) :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s))) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (fun (i : ι) => Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) f)))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) -> (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (fun (i : ι) => Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f)))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) -> (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (fun (i : ι) => Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f)))
 Case conversion may be inaccurate. Consider using '#align lagrange.eq_interpolate Lagrange.eq_interpolateₓ'. -/
 theorem eq_interpolate {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree < s.card) :
     f = interpolate s v fun i => f.eval (v i) :=
@@ -554,7 +554,7 @@ theorem eq_interpolate {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s))) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) f) (r i))) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u2} F (Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f) (r i))) -> (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u2} F (Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f) (r i))) -> (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r))
 Case conversion may be inaccurate. Consider using '#align lagrange.eq_interpolate_of_eval_eq Lagrange.eq_interpolate_of_eval_eqₓ'. -/
 theorem eq_interpolate_of_eval_eq {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree < s.card)
     (eval_f : ∀ i ∈ s, f.eval (v i) = r i) : f = interpolate s v r :=
@@ -567,7 +567,7 @@ theorem eq_interpolate_of_eval_eq {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Iff (And (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s))) (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) f) (r i)))) (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (Iff (And (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u2} F (Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f) (r i)))) (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (Iff (And (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u2} F (Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f) (r i)))) (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)))
 Case conversion may be inaccurate. Consider using '#align lagrange.eq_interpolate_iff Lagrange.eq_interpolate_iffₓ'. -/
 /-- This is the characteristic property of the interpolation: the interpolation is the
 unique polynomial of `degree < fintype.card ι` which takes the value of the `r i` on the `v i`.
@@ -610,7 +610,7 @@ def funEquivDegreeLT (hvs : Set.InjOn v s) : degreeLT F s.card ≃ₗ[F] s → F
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {t : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) t)) -> (Finset.Nonempty.{u2} ι s) -> (HasSubset.Subset.{u2} (Finset.{u2} ι) (Finset.hasSubset.{u2} ι) s t) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) t v) r) (Finset.sum.{u1, u2} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) ι (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Insert.insert.{u2, u2} ι (Finset.{u2} ι) (Finset.hasInsert.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) i (SDiff.sdiff.{u2} (Finset.{u2} ι) (Finset.hasSdiff.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) t s)) v) r) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {t : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι t)) -> (Finset.Nonempty.{u2} ι s) -> (HasSubset.Subset.{u2} (Finset.{u2} ι) (Finset.instHasSubsetFinset.{u2} ι) s t) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) t v) r) (Finset.sum.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Insert.insert.{u2, u2} ι (Finset.{u2} ι) (Finset.instInsertFinset.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) i (SDiff.sdiff.{u2} (Finset.{u2} ι) (Finset.instSDiffFinset.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) t s)) v) r) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {t : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι t)) -> (Finset.Nonempty.{u2} ι s) -> (HasSubset.Subset.{u2} (Finset.{u2} ι) (Finset.instHasSubsetFinset.{u2} ι) s t) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) t v) r) (Finset.sum.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Insert.insert.{u2, u2} ι (Finset.{u2} ι) (Finset.instInsertFinset.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) i (SDiff.sdiff.{u2} (Finset.{u2} ι) (Finset.instSDiffFinset.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) t s)) v) r) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_sum_interpolate_insert_sdiff Lagrange.interpolate_eq_sum_interpolate_insert_sdiffₓ'. -/
 theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs : s.Nonempty)
     (hst : s ⊆ t) :
@@ -654,7 +654,7 @@ theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {j : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) j s) -> (Ne.{succ u2} ι i j) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F 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(Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F 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(DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r) (Lagrange.basisDivisor.{u1} F _inst_1 (v j) (v i)))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {j : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) j s) -> (Ne.{succ u2} ι i j) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.add'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s j) v) r) (Lagrange.basisDivisor.{u1} F _inst_1 (v i) (v j))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r) (Lagrange.basisDivisor.{u1} F _inst_1 (v j) (v i)))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {j : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) j s) -> (Ne.{succ u2} ι i j) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F 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(Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r) (Lagrange.basisDivisor.{u1} F _inst_1 (v j) (v i)))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_add_interpolate_erase Lagrange.interpolate_eq_add_interpolate_eraseₓ'. -/
 theorem interpolate_eq_add_interpolate_erase (hvs : Set.InjOn v s) (hi : i ∈ s) (hj : j ∈ s)
     (hij : i ≠ j) :
@@ -696,7 +696,7 @@ def nodal (s : Finset ι) (v : ι → F) : F[X] :=
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} (s : Finset.{u2} ι) (v : ι -> F), Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v) (Finset.prod.{u1, u2} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.commRing.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)))) s (fun (i : ι) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (v i))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} (s : Finset.{u2} ι) (v : ι -> F), Eq.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v) (Finset.prod.{u1, u2} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.commRing.{u1} F (Field.toCommRing.{u1} F _inst_1))) s (fun (i : ι) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i)) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} (s : Finset.{u2} ι) (v : ι -> F), Eq.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v) (Finset.prod.{u1, u2} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.commRing.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)))) s (fun (i : ι) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i)) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i))))
 Case conversion may be inaccurate. Consider using '#align lagrange.nodal_eq Lagrange.nodal_eqₓ'. -/
 theorem nodal_eq (s : Finset ι) (v : ι → F) : nodal s v = ∏ i in s, X - C (v i) :=
   rfl
@@ -771,7 +771,7 @@ theorem nodal_eq_mul_nodal_erase [DecidableEq ι] (hi : i ∈ s) :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {i : ι} (v : ι -> F), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Dvd.Dvd.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.commRing.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1))))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (v i))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {i : ι} (v : ι -> F), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Dvd.dvd.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.commRing.{u1} F (Field.toCommRing.{u1} F _inst_1)))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i)) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {i : ι} (v : ι -> F), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Dvd.dvd.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.commRing.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1))))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i)) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v))
 Case conversion may be inaccurate. Consider using '#align lagrange.X_sub_C_dvd_nodal Lagrange.X_sub_C_dvd_nodalₓ'. -/
 theorem X_sub_C_dvd_nodal (v : ι → F) (hi : i ∈ s) : X - C (v i) ∣ nodal s v :=
   ⟨_, by classical exact nodal_eq_mul_nodal_erase hi⟩
@@ -905,7 +905,7 @@ theorem eval_basis_not_at_node (hi : i ∈ s) (hxi : x ≠ v i) :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) [_inst_2 : DecidableEq.{succ u2} ι], Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (Finset.sum.{u1, u2} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) ι (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.hasDiv.{u1} F _inst_1)) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (v i))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (r i))))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) [_inst_2 : DecidableEq.{succ u1} ι], Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (Finset.sum.{u2, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (NonAssocRing.toNonUnitalNonAssocRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Ring.toNonAssocRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (CommRing.toRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (EuclideanDomain.toCommRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (HDiv.hDiv.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHDiv.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instDivPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1)) (Lagrange.nodal.{u2, u1} F _inst_1 ι s v) (HSub.hSub.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (v i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHSub.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.sub.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (Polynomial.X.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (v i))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i))))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) [_inst_2 : DecidableEq.{succ u1} ι], Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (Finset.sum.{u2, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (NonAssocRing.toNonUnitalNonAssocRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Ring.toNonAssocRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (CommRing.toRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (EuclideanDomain.toCommRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (HDiv.hDiv.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHDiv.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instDivPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1)) (Lagrange.nodal.{u2, u1} F _inst_1 ι s v) (HSub.hSub.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (v i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHSub.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.sub.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (Polynomial.X.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (v i))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_nodal_weight_mul_nodal_div_X_sub_C Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_Cₓ'. -/
 theorem interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C :
     interpolate s v r = ∑ i in s, C (nodalWeight s v i) * (nodal s v / (X - C (v i))) * C (r i) :=
@@ -916,7 +916,7 @@ theorem interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) x (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) x (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)) (Finset.sum.{u1, u2} F ι (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (DivInvMonoid.toHasInv.{u1} F (DivisionRing.toDivInvMonoid.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toHasSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (AddGroupWithOne.toAddGroup.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))) x (v i)))) (r i)))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))) (r i)))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))) (r i)))))
 Case conversion may be inaccurate. Consider using '#align lagrange.eval_interpolate_not_at_node Lagrange.eval_interpolate_not_at_nodeₓ'. -/
 /-- This is the first barycentric form of the Lagrange interpolant. -/
 theorem eval_interpolate_not_at_node (hx : ∀ i ∈ s, x ≠ v i) :
@@ -945,7 +945,7 @@ theorem sum_nodalWeight_mul_inv_sub_ne_zero (hvs : Set.InjOn v s) (hx : ∀ i 
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Finset.Nonempty.{u2} ι s) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) x (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HDiv.hDiv.{u1, u1, u1} F F F (instHDiv.{u1} F (DivInvMonoid.toHasDiv.{u1} F (DivisionRing.toDivInvMonoid.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Finset.sum.{u1, u2} F ι (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (DivInvMonoid.toHasInv.{u1} F (DivisionRing.toDivInvMonoid.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toHasSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (AddGroupWithOne.toAddGroup.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))) x (v i)))) (r i))) (Finset.sum.{u1, u2} F ι (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (DivInvMonoid.toHasInv.{u1} F (DivisionRing.toDivInvMonoid.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toHasSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (AddGroupWithOne.toAddGroup.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))) x (v i)))))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Finset.Nonempty.{u2} ι s) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HDiv.hDiv.{u1, u1, u1} F F F (instHDiv.{u1} F (Field.toDiv.{u1} F _inst_1)) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))) (r i))) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Finset.Nonempty.{u2} ι s) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2519 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HDiv.hDiv.{u1, u1, u1} F F F (instHDiv.{u1} F (Field.toDiv.{u1} F _inst_1)) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))) (r i))) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))))))
 Case conversion may be inaccurate. Consider using '#align lagrange.eval_interpolate_not_at_node' Lagrange.eval_interpolate_not_at_node'ₓ'. -/
 /-- This is the second barycentric form of the Lagrange interpolant. -/
 theorem eval_interpolate_not_at_node' (hvs : Set.InjOn v s) (hs : s.Nonempty)

b5ad1414

bump to nightly-2023-05-09-13

mathlib commit https://github.com/leanprover-community/mathlib/commit/d4437c68c8d350fc9d4e95e1e174409db35e30d7

6ff25244

Diff

@@ -415,7 +415,7 @@ def interpolate (s : Finset ι) (v : ι → F) : (ι → F) →ₗ[F] F[X]
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {v : ι -> F} (r : ι -> F), Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (EmptyCollection.emptyCollection.{u2} (Finset.{u2} ι) (Finset.hasEmptyc.{u2} ι)) v) r) (OfNat.ofNat.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.zero.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {v : ι -> F} (r : ι -> F), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (EmptyCollection.emptyCollection.{u1} (Finset.{u1} ι) (Finset.instEmptyCollectionFinset.{u1} ι)) v) r) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Polynomial.zero.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {v : ι -> F} (r : ι -> F), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (EmptyCollection.emptyCollection.{u1} (Finset.{u1} ι) (Finset.instEmptyCollectionFinset.{u1} ι)) v) r) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Polynomial.zero.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_empty Lagrange.interpolate_emptyₓ'. -/
 @[simp]
 theorem interpolate_empty : interpolate ∅ v r = 0 := by rw [interpolate_apply, sum_empty]
@@ -425,7 +425,7 @@ theorem interpolate_empty : interpolate ∅ v r = 0 := by rw [interpolate_apply,
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {i : ι} {v : ι -> F} (r : ι -> F), Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Singleton.singleton.{u2, u2} ι (Finset.{u2} ι) (Finset.hasSingleton.{u2} ι) i) v) r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (r i))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {i : ι} {v : ι -> F} (r : ι -> F), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Singleton.singleton.{u1, u1} ι (Finset.{u1} ι) (Finset.instSingletonFinset.{u1} ι) i) v) r) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {i : ι} {v : ι -> F} (r : ι -> F), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Singleton.singleton.{u1, u1} ι (Finset.{u1} ι) (Finset.instSingletonFinset.{u1} ι) i) v) r) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_singleton Lagrange.interpolate_singletonₓ'. -/
 @[simp]
 theorem interpolate_singleton : interpolate {i} v r = C (r i) := by
@@ -436,7 +436,7 @@ theorem interpolate_singleton : interpolate {i} v r = C (r i) := by
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F}, (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Finset.Nonempty.{u2} ι s) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (OfNat.ofNat.{max u2 u1} (ι -> F) 1 (OfNat.mk.{max u2 u1} (ι -> F) 1 (One.one.{max u2 u1} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddMonoidWithOne.toOne.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) (OfNat.ofNat.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 1 (OfNat.mk.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 1 (One.one.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.hasOne.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F}, (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Finset.Nonempty.{u2} ι s) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Polynomial.one.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F}, (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Finset.Nonempty.{u2} ι s) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Polynomial.one.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_one Lagrange.interpolate_oneₓ'. -/
 theorem interpolate_one (hvs : Set.InjOn v s) (hs : s.Nonempty) : interpolate s v 1 = 1 :=
   by
@@ -448,7 +448,7 @@ theorem interpolate_one (hvs : Set.InjOn v s) (hs : s.Nonempty) : interpolate s
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (r i))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (v i) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (r i))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (v i) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (r i))
 Case conversion may be inaccurate. Consider using '#align lagrange.eval_interpolate_at_node Lagrange.eval_interpolate_at_nodeₓ'. -/
 theorem eval_interpolate_at_node (hvs : Set.InjOn v s) (hi : i ∈ s) :
     eval (v i) (interpolate s v r) = r i :=
@@ -463,7 +463,7 @@ theorem eval_interpolate_at_node (hvs : Set.InjOn v s) (hi : i ∈ s) :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
 Case conversion may be inaccurate. Consider using '#align lagrange.degree_interpolate_le Lagrange.degree_interpolate_leₓ'. -/
 theorem degree_interpolate_le (hvs : Set.InjOn v s) : (interpolate s v r).degree ≤ ↑(s.card - 1) :=
   by
@@ -480,7 +480,7 @@ theorem degree_interpolate_le (hvs : Set.InjOn v s) : (interpolate s v r).degree
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s)))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u2} ι s)))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u2} ι s)))
 Case conversion may be inaccurate. Consider using '#align lagrange.degree_interpolate_lt Lagrange.degree_interpolate_ltₓ'. -/
 theorem degree_interpolate_lt (hvs : Set.InjOn v s) : (interpolate s v r).degree < s.card :=
   by
@@ -496,7 +496,7 @@ theorem degree_interpolate_lt (hvs : Set.InjOn v s) : (interpolate s v r).degree
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
 Case conversion may be inaccurate. Consider using '#align lagrange.degree_interpolate_erase_lt Lagrange.degree_interpolate_erase_ltₓ'. -/
 theorem degree_interpolate_erase_lt (hvs : Set.InjOn v s) (hi : i ∈ s) :
     (interpolate (s.eraseₓ i) v r).degree < ↑(s.card - 1) :=
@@ -509,7 +509,7 @@ theorem degree_interpolate_erase_lt (hvs : Set.InjOn v s) (hi : i ∈ s) :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F 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(DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F 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(DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i)))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i)))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i)))
 Case conversion may be inaccurate. Consider using '#align lagrange.values_eq_on_of_interpolate_eq Lagrange.values_eq_on_of_interpolate_eqₓ'. -/
 theorem values_eq_on_of_interpolate_eq (hvs : Set.InjOn v s)
     (hrr' : interpolate s v r = interpolate s v r') : ∀ i ∈ s, r i = r' i := fun _ hi => by
@@ -520,7 +520,7 @@ theorem values_eq_on_of_interpolate_eq (hvs : Set.InjOn v s)
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r'))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r'))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} 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(Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F 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(Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F 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(Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r'))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_of_values_eq_on Lagrange.interpolate_eq_of_values_eq_onₓ'. -/
 theorem interpolate_eq_of_values_eq_on (hrr' : ∀ i ∈ s, r i = r' i) :
     interpolate s v r = interpolate s v r' :=
@@ -531,7 +531,7 @@ theorem interpolate_eq_of_values_eq_on (hrr' : ∀ i ∈ s, r i = r' i) :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Iff (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F 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_inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) 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(Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_iff_values_eq_on Lagrange.interpolate_eq_iff_values_eq_onₓ'. -/
 theorem interpolate_eq_iff_values_eq_on (hvs : Set.InjOn v s) :
     interpolate s v r = interpolate s v r' ↔ ∀ i ∈ s, r i = r' i :=
@@ -542,7 +542,7 @@ theorem interpolate_eq_iff_values_eq_on (hvs : Set.InjOn v s) :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s))) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (fun (i : ι) => Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) f)))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) -> (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (fun (i : ι) => Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f)))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) -> (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (fun (i : ι) => Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f)))
 Case conversion may be inaccurate. Consider using '#align lagrange.eq_interpolate Lagrange.eq_interpolateₓ'. -/
 theorem eq_interpolate {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree < s.card) :
     f = interpolate s v fun i => f.eval (v i) :=
@@ -554,7 +554,7 @@ theorem eq_interpolate {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s))) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) f) (r i))) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u2} F (Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f) (r i))) -> (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u2} F (Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f) (r i))) -> (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r))
 Case conversion may be inaccurate. Consider using '#align lagrange.eq_interpolate_of_eval_eq Lagrange.eq_interpolate_of_eval_eqₓ'. -/
 theorem eq_interpolate_of_eval_eq {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree < s.card)
     (eval_f : ∀ i ∈ s, f.eval (v i) = r i) : f = interpolate s v r :=
@@ -567,7 +567,7 @@ theorem eq_interpolate_of_eval_eq {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Iff (And (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s))) (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) f) (r i)))) (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (Iff (And (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u2} F (Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f) (r i)))) (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (Iff (And (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u2} F (Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f) (r i)))) (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)))
 Case conversion may be inaccurate. Consider using '#align lagrange.eq_interpolate_iff Lagrange.eq_interpolate_iffₓ'. -/
 /-- This is the characteristic property of the interpolation: the interpolation is the
 unique polynomial of `degree < fintype.card ι` which takes the value of the `r i` on the `v i`.
@@ -610,7 +610,7 @@ def funEquivDegreeLT (hvs : Set.InjOn v s) : degreeLT F s.card ≃ₗ[F] s → F
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {t : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) t)) -> (Finset.Nonempty.{u2} ι s) -> (HasSubset.Subset.{u2} (Finset.{u2} ι) (Finset.hasSubset.{u2} ι) s t) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) t v) r) (Finset.sum.{u1, u2} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) ι (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Insert.insert.{u2, u2} ι (Finset.{u2} ι) (Finset.hasInsert.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) i (SDiff.sdiff.{u2} (Finset.{u2} ι) (Finset.hasSdiff.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) t s)) v) r) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {t : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι t)) -> (Finset.Nonempty.{u2} ι s) -> (HasSubset.Subset.{u2} (Finset.{u2} ι) (Finset.instHasSubsetFinset.{u2} ι) s t) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) t v) r) (Finset.sum.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Insert.insert.{u2, u2} ι (Finset.{u2} ι) (Finset.instInsertFinset.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) i (SDiff.sdiff.{u2} (Finset.{u2} ι) (Finset.instSDiffFinset.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) t s)) v) r) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {t : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι t)) -> (Finset.Nonempty.{u2} ι s) -> (HasSubset.Subset.{u2} (Finset.{u2} ι) (Finset.instHasSubsetFinset.{u2} ι) s t) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) t v) r) (Finset.sum.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Insert.insert.{u2, u2} ι (Finset.{u2} ι) (Finset.instInsertFinset.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) i (SDiff.sdiff.{u2} (Finset.{u2} ι) (Finset.instSDiffFinset.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) t s)) v) r) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_sum_interpolate_insert_sdiff Lagrange.interpolate_eq_sum_interpolate_insert_sdiffₓ'. -/
 theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs : s.Nonempty)
     (hst : s ⊆ t) :
@@ -654,7 +654,7 @@ theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {j : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) j s) -> (Ne.{succ u2} ι i j) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => 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(DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r) (Lagrange.basisDivisor.{u1} F _inst_1 (v j) (v i)))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {j : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) j s) -> (Ne.{succ u2} ι i j) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.add'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s j) v) r) (Lagrange.basisDivisor.{u1} F _inst_1 (v i) (v j))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r) (Lagrange.basisDivisor.{u1} F _inst_1 (v j) (v i)))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {j : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) j s) -> (Ne.{succ u2} ι i j) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.add'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F 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(Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F 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(Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s j) v) r) (Lagrange.basisDivisor.{u1} F _inst_1 (v i) (v j))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => 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(Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) 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(DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r) (Lagrange.basisDivisor.{u1} F _inst_1 (v j) (v i)))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_add_interpolate_erase Lagrange.interpolate_eq_add_interpolate_eraseₓ'. -/
 theorem interpolate_eq_add_interpolate_erase (hvs : Set.InjOn v s) (hi : i ∈ s) (hj : j ∈ s)
     (hij : i ≠ j) :
@@ -905,7 +905,7 @@ theorem eval_basis_not_at_node (hi : i ∈ s) (hxi : x ≠ v i) :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) [_inst_2 : DecidableEq.{succ u2} ι], Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (Finset.sum.{u1, u2} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) ι (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.hasDiv.{u1} F _inst_1)) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (v i))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (r i))))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) [_inst_2 : DecidableEq.{succ u1} ι], Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (Finset.sum.{u2, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (NonAssocRing.toNonUnitalNonAssocRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Ring.toNonAssocRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (CommRing.toRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (EuclideanDomain.toCommRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (HDiv.hDiv.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHDiv.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instDivPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1)) (Lagrange.nodal.{u2, u1} F _inst_1 ι s v) (HSub.hSub.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (v i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHSub.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.sub.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (Polynomial.X.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (v i))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i))))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) [_inst_2 : DecidableEq.{succ u1} ι], Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (Finset.sum.{u2, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (NonAssocRing.toNonUnitalNonAssocRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Ring.toNonAssocRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (CommRing.toRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (EuclideanDomain.toCommRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (HDiv.hDiv.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHDiv.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instDivPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1)) (Lagrange.nodal.{u2, u1} F _inst_1 ι s v) (HSub.hSub.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (v i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHSub.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.sub.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (Polynomial.X.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (v i))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_nodal_weight_mul_nodal_div_X_sub_C Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_Cₓ'. -/
 theorem interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C :
     interpolate s v r = ∑ i in s, C (nodalWeight s v i) * (nodal s v / (X - C (v i))) * C (r i) :=
@@ -916,7 +916,7 @@ theorem interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) x (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) x (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)) (Finset.sum.{u1, u2} F ι (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (DivInvMonoid.toHasInv.{u1} F (DivisionRing.toDivInvMonoid.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toHasSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (AddGroupWithOne.toAddGroup.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))) x (v i)))) (r i)))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))) (r i)))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))) (r i)))))
 Case conversion may be inaccurate. Consider using '#align lagrange.eval_interpolate_not_at_node Lagrange.eval_interpolate_not_at_nodeₓ'. -/
 /-- This is the first barycentric form of the Lagrange interpolant. -/
 theorem eval_interpolate_not_at_node (hx : ∀ i ∈ s, x ≠ v i) :
@@ -945,7 +945,7 @@ theorem sum_nodalWeight_mul_inv_sub_ne_zero (hvs : Set.InjOn v s) (hx : ∀ i 
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Finset.Nonempty.{u2} ι s) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) x (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HDiv.hDiv.{u1, u1, u1} F F F (instHDiv.{u1} F (DivInvMonoid.toHasDiv.{u1} F (DivisionRing.toDivInvMonoid.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Finset.sum.{u1, u2} F ι (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (DivInvMonoid.toHasInv.{u1} F (DivisionRing.toDivInvMonoid.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toHasSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (AddGroupWithOne.toAddGroup.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))) x (v i)))) (r i))) (Finset.sum.{u1, u2} F ι (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (DivInvMonoid.toHasInv.{u1} F (DivisionRing.toDivInvMonoid.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toHasSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (AddGroupWithOne.toAddGroup.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))) x (v i)))))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Finset.Nonempty.{u2} ι s) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HDiv.hDiv.{u1, u1, u1} F F F (instHDiv.{u1} F (Field.toDiv.{u1} F _inst_1)) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))) (r i))) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Finset.Nonempty.{u2} ι s) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2534 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HDiv.hDiv.{u1, u1, u1} F F F (instHDiv.{u1} F (Field.toDiv.{u1} F _inst_1)) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))) (r i))) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))))))
 Case conversion may be inaccurate. Consider using '#align lagrange.eval_interpolate_not_at_node' Lagrange.eval_interpolate_not_at_node'ₓ'. -/
 /-- This is the second barycentric form of the Lagrange interpolant. -/
 theorem eval_interpolate_not_at_node' (hvs : Set.InjOn v s) (hs : s.Nonempty)

b5ad1414

bump to nightly-2023-05-08-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

63e712c6

Diff

@@ -55,7 +55,7 @@ variable (s : Finset R)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} (s : Finset.{u1} R), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u1} R s))) -> (forall (x : R), (Membership.Mem.{u1, u1} R (Finset.{u1} R) (Finset.hasMem.{u1} R) x s) -> (Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x f) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} (s : Finset.{u1} R), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} R s))) -> (forall (x : R), (Membership.mem.{u1, u1} R (Finset.{u1} R) (Finset.instMembershipFinset.{u1} R) x s) -> (Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x f) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} (s : Finset.{u1} R), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} R s))) -> (forall (x : R), (Membership.mem.{u1, u1} R (Finset.{u1} R) (Finset.instMembershipFinset.{u1} R) x s) -> (Eq.{succ u1} R (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) x f) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) f (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eq_zero_of_degree_lt_of_eval_finset_eq_zero Polynomial.eq_zero_of_degree_lt_of_eval_finset_eq_zeroₓ'. -/
 theorem eq_zero_of_degree_lt_of_eval_finset_eq_zero (degree_f_lt : f.degree < s.card)
     (eval_f : ∀ x ∈ s, f.eval x = 0) : f = 0 :=
@@ -102,7 +102,7 @@ variable {ι : Type _} {v : ι → R} (s : Finset ι)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {ι : Type.{u2}} {v : ι -> R} (s : Finset.{u2} ι), (Set.InjOn.{u2, u1} ι R v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s))) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (v i) f) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {ι : Type.{u2}} {v : ι -> R} (s : Finset.{u2} ι), (Set.InjOn.{u2, u1} ι R v (Finset.toSet.{u2} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u2} ι s))) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (v i) f) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {ι : Type.{u2}} {v : ι -> R} (s : Finset.{u2} ι), (Set.InjOn.{u2, u1} ι R v (Finset.toSet.{u2} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u2} ι s))) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} R (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (v i) f) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) f (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zero Polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zeroₓ'. -/
 theorem eq_zero_of_degree_lt_of_eval_index_eq_zero (hvs : Set.InjOn v s)
     (degree_f_lt : f.degree < s.card) (eval_f : ∀ i ∈ s, f.eval (v i) = 0) : f = 0 := by
@@ -232,7 +232,7 @@ theorem eval_basisDivisor_right : eval y (basisDivisor x y) = 0 := by
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {x : F} {y : F}, (Ne.{succ u1} F x y) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) x (Lagrange.basisDivisor.{u1} F _inst_1 x y)) (OfNat.ofNat.{u1} F 1 (OfNat.mk.{u1} F 1 (One.one.{u1} F (AddMonoidWithOne.toOne.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {x : F} {y : F}, (Ne.{succ u1} F x y) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (Lagrange.basisDivisor.{u1} F _inst_1 x y)) (OfNat.ofNat.{u1} F 1 (One.toOfNat1.{u1} F (NonAssocRing.toOne.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {x : F} {y : F}, (Ne.{succ u1} F x y) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (Lagrange.basisDivisor.{u1} F _inst_1 x y)) (OfNat.ofNat.{u1} F 1 (One.toOfNat1.{u1} F (Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align lagrange.eval_basis_divisor_left_of_ne Lagrange.eval_basisDivisor_left_of_neₓ'. -/
 theorem eval_basisDivisor_left_of_ne (hxy : x ≠ y) : eval x (basisDivisor x y) = 1 :=
   by
@@ -310,7 +310,7 @@ theorem basis_ne_zero (hvs : Set.InjOn v s) (hi : i ∈ s) : Lagrange.basis s v
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} {i : ι}, (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (OfNat.ofNat.{u1} F 1 (OfNat.mk.{u1} F 1 (One.one.{u1} F (AddMonoidWithOne.toOne.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} {i : ι}, (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (v i) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (OfNat.ofNat.{u1} F 1 (One.toOfNat1.{u1} F (NonAssocRing.toOne.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} {i : ι}, (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (v i) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (OfNat.ofNat.{u1} F 1 (One.toOfNat1.{u1} F (Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align lagrange.eval_basis_self Lagrange.eval_basis_selfₓ'. -/
 @[simp]
 theorem eval_basis_self (hvs : Set.InjOn v s) (hi : i ∈ s) :
@@ -415,7 +415,7 @@ def interpolate (s : Finset ι) (v : ι → F) : (ι → F) →ₗ[F] F[X]
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {v : ι -> F} (r : ι -> F), Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (EmptyCollection.emptyCollection.{u2} (Finset.{u2} ι) (Finset.hasEmptyc.{u2} ι)) v) r) (OfNat.ofNat.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.zero.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {v : ι -> F} (r : ι -> F), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (EmptyCollection.emptyCollection.{u1} (Finset.{u1} ι) (Finset.instEmptyCollectionFinset.{u1} ι)) v) r) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Polynomial.zero.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {v : ι -> F} (r : ι -> F), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (EmptyCollection.emptyCollection.{u1} (Finset.{u1} ι) (Finset.instEmptyCollectionFinset.{u1} ι)) v) r) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Polynomial.zero.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_empty Lagrange.interpolate_emptyₓ'. -/
 @[simp]
 theorem interpolate_empty : interpolate ∅ v r = 0 := by rw [interpolate_apply, sum_empty]
@@ -425,7 +425,7 @@ theorem interpolate_empty : interpolate ∅ v r = 0 := by rw [interpolate_apply,
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {i : ι} {v : ι -> F} (r : ι -> F), Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Singleton.singleton.{u2, u2} ι (Finset.{u2} ι) (Finset.hasSingleton.{u2} ι) i) v) r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (r i))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {i : ι} {v : ι -> F} (r : ι -> F), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Singleton.singleton.{u1, u1} ι (Finset.{u1} ι) (Finset.instSingletonFinset.{u1} ι) i) v) r) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {i : ι} {v : ι -> F} (r : ι -> F), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Singleton.singleton.{u1, u1} ι (Finset.{u1} ι) (Finset.instSingletonFinset.{u1} ι) i) v) r) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_singleton Lagrange.interpolate_singletonₓ'. -/
 @[simp]
 theorem interpolate_singleton : interpolate {i} v r = C (r i) := by
@@ -436,7 +436,7 @@ theorem interpolate_singleton : interpolate {i} v r = C (r i) := by
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F}, (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Finset.Nonempty.{u2} ι s) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (OfNat.ofNat.{max u2 u1} (ι -> F) 1 (OfNat.mk.{max u2 u1} (ι -> F) 1 (One.one.{max u2 u1} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddMonoidWithOne.toOne.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) (OfNat.ofNat.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 1 (OfNat.mk.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 1 (One.one.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.hasOne.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F}, (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Finset.Nonempty.{u2} ι s) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonAssocRing.toOne.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonAssocRing.toOne.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonAssocRing.toOne.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonAssocRing.toOne.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))) (Polynomial.one.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F}, (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Finset.Nonempty.{u2} ι s) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (OfNat.ofNat.{max u1 u2} (ι -> F) 1 (One.toOfNat1.{max u1 u2} (ι -> F) (Pi.instOne.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => Semiring.toOne.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Polynomial.one.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_one Lagrange.interpolate_oneₓ'. -/
 theorem interpolate_one (hvs : Set.InjOn v s) (hs : s.Nonempty) : interpolate s v 1 = 1 :=
   by
@@ -448,7 +448,7 @@ theorem interpolate_one (hvs : Set.InjOn v s) (hs : s.Nonempty) : interpolate s
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (r i))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (v i) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (r i))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (v i) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (r i))
 Case conversion may be inaccurate. Consider using '#align lagrange.eval_interpolate_at_node Lagrange.eval_interpolate_at_nodeₓ'. -/
 theorem eval_interpolate_at_node (hvs : Set.InjOn v s) (hi : i ∈ s) :
     eval (v i) (interpolate s v r) = r i :=
@@ -463,7 +463,7 @@ theorem eval_interpolate_at_node (hvs : Set.InjOn v s) (hi : i ∈ s) :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
 Case conversion may be inaccurate. Consider using '#align lagrange.degree_interpolate_le Lagrange.degree_interpolate_leₓ'. -/
 theorem degree_interpolate_le (hvs : Set.InjOn v s) : (interpolate s v r).degree ≤ ↑(s.card - 1) :=
   by
@@ -480,7 +480,7 @@ theorem degree_interpolate_le (hvs : Set.InjOn v s) : (interpolate s v r).degree
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s)))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u2} ι s)))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u2} ι s)))
 Case conversion may be inaccurate. Consider using '#align lagrange.degree_interpolate_lt Lagrange.degree_interpolate_ltₓ'. -/
 theorem degree_interpolate_lt (hvs : Set.InjOn v s) : (interpolate s v r).degree < s.card :=
   by
@@ -496,7 +496,7 @@ theorem degree_interpolate_lt (hvs : Set.InjOn v s) : (interpolate s v r).degree
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
 Case conversion may be inaccurate. Consider using '#align lagrange.degree_interpolate_erase_lt Lagrange.degree_interpolate_erase_ltₓ'. -/
 theorem degree_interpolate_erase_lt (hvs : Set.InjOn v s) (hi : i ∈ s) :
     (interpolate (s.eraseₓ i) v r).degree < ↑(s.card - 1) :=
@@ -509,7 +509,7 @@ theorem degree_interpolate_erase_lt (hvs : Set.InjOn v s) (hi : i ∈ s) :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F 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(DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F 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(DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i)))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i)))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i)))
 Case conversion may be inaccurate. Consider using '#align lagrange.values_eq_on_of_interpolate_eq Lagrange.values_eq_on_of_interpolate_eqₓ'. -/
 theorem values_eq_on_of_interpolate_eq (hvs : Set.InjOn v s)
     (hrr' : interpolate s v r = interpolate s v r') : ∀ i ∈ s, r i = r' i := fun _ hi => by
@@ -520,7 +520,7 @@ theorem values_eq_on_of_interpolate_eq (hvs : Set.InjOn v s)
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r'))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r'))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} 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(Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F 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(Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r'))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_of_values_eq_on Lagrange.interpolate_eq_of_values_eq_onₓ'. -/
 theorem interpolate_eq_of_values_eq_on (hrr' : ∀ i ∈ s, r i = r' i) :
     interpolate s v r = interpolate s v r' :=
@@ -531,7 +531,7 @@ theorem interpolate_eq_of_values_eq_on (hrr' : ∀ i ∈ s, r i = r' i) :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Iff (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F 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_inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F 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(LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_iff_values_eq_on Lagrange.interpolate_eq_iff_values_eq_onₓ'. -/
 theorem interpolate_eq_iff_values_eq_on (hvs : Set.InjOn v s) :
     interpolate s v r = interpolate s v r' ↔ ∀ i ∈ s, r i = r' i :=
@@ -542,7 +542,7 @@ theorem interpolate_eq_iff_values_eq_on (hvs : Set.InjOn v s) :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s))) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (fun (i : ι) => Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) f)))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) -> (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (fun (i : ι) => Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f)))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) -> (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (fun (i : ι) => Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f)))
 Case conversion may be inaccurate. Consider using '#align lagrange.eq_interpolate Lagrange.eq_interpolateₓ'. -/
 theorem eq_interpolate {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree < s.card) :
     f = interpolate s v fun i => f.eval (v i) :=
@@ -554,7 +554,7 @@ theorem eq_interpolate {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s))) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) f) (r i))) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u2} F (Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f) (r i))) -> (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u2} F (Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f) (r i))) -> (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r))
 Case conversion may be inaccurate. Consider using '#align lagrange.eq_interpolate_of_eval_eq Lagrange.eq_interpolate_of_eval_eqₓ'. -/
 theorem eq_interpolate_of_eval_eq {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree < s.card)
     (eval_f : ∀ i ∈ s, f.eval (v i) = r i) : f = interpolate s v r :=
@@ -567,7 +567,7 @@ theorem eq_interpolate_of_eval_eq {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Iff (And (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s))) (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) f) (r i)))) (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (Iff (And (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u2} F (Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f) (r i)))) (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (Iff (And (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u2} F (Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f) (r i)))) (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)))
 Case conversion may be inaccurate. Consider using '#align lagrange.eq_interpolate_iff Lagrange.eq_interpolate_iffₓ'. -/
 /-- This is the characteristic property of the interpolation: the interpolation is the
 unique polynomial of `degree < fintype.card ι` which takes the value of the `r i` on the `v i`.
@@ -610,7 +610,7 @@ def funEquivDegreeLT (hvs : Set.InjOn v s) : degreeLT F s.card ≃ₗ[F] s → F
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {t : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) t)) -> (Finset.Nonempty.{u2} ι s) -> (HasSubset.Subset.{u2} (Finset.{u2} ι) (Finset.hasSubset.{u2} ι) s t) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) t v) r) (Finset.sum.{u1, u2} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) ι (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Insert.insert.{u2, u2} ι (Finset.{u2} ι) (Finset.hasInsert.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) i (SDiff.sdiff.{u2} (Finset.{u2} ι) (Finset.hasSdiff.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) t s)) v) r) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {t : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι t)) -> (Finset.Nonempty.{u2} ι s) -> (HasSubset.Subset.{u2} (Finset.{u2} ι) (Finset.instHasSubsetFinset.{u2} ι) s t) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) t v) r) (Finset.sum.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Insert.insert.{u2, u2} ι (Finset.{u2} ι) (Finset.instInsertFinset.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) i (SDiff.sdiff.{u2} (Finset.{u2} ι) (Finset.instSDiffFinset.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) t s)) v) r) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {t : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι t)) -> (Finset.Nonempty.{u2} ι s) -> (HasSubset.Subset.{u2} (Finset.{u2} ι) (Finset.instHasSubsetFinset.{u2} ι) s t) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) t v) r) (Finset.sum.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Insert.insert.{u2, u2} ι (Finset.{u2} ι) (Finset.instInsertFinset.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) i (SDiff.sdiff.{u2} (Finset.{u2} ι) (Finset.instSDiffFinset.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) t s)) v) r) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_sum_interpolate_insert_sdiff Lagrange.interpolate_eq_sum_interpolate_insert_sdiffₓ'. -/
 theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs : s.Nonempty)
     (hst : s ⊆ t) :
@@ -654,7 +654,7 @@ theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {j : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) j s) -> (Ne.{succ u2} ι i j) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => 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(DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r) (Lagrange.basisDivisor.{u1} F _inst_1 (v j) (v i)))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {j : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) j s) -> (Ne.{succ u2} ι i j) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.add'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s j) v) r) (Lagrange.basisDivisor.{u1} F _inst_1 (v i) (v j))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r) (Lagrange.basisDivisor.{u1} F _inst_1 (v j) (v i)))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {j : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) j s) -> (Ne.{succ u2} ι i j) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.add'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F 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(Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s j) v) r) (Lagrange.basisDivisor.{u1} F _inst_1 (v i) (v j))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r) (Lagrange.basisDivisor.{u1} F _inst_1 (v j) (v i)))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_add_interpolate_erase Lagrange.interpolate_eq_add_interpolate_eraseₓ'. -/
 theorem interpolate_eq_add_interpolate_erase (hvs : Set.InjOn v s) (hi : i ∈ s) (hj : j ∈ s)
     (hij : i ≠ j) :
@@ -696,7 +696,7 @@ def nodal (s : Finset ι) (v : ι → F) : F[X] :=
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} (s : Finset.{u2} ι) (v : ι -> F), Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v) (Finset.prod.{u1, u2} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.commRing.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)))) s (fun (i : ι) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (v i))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} (s : Finset.{u2} ι) (v : ι -> F), Eq.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v) (Finset.prod.{u1, u2} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1))) s (fun (i : ι) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i)) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} (s : Finset.{u2} ι) (v : ι -> F), Eq.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v) (Finset.prod.{u1, u2} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.commRing.{u1} F (Field.toCommRing.{u1} F _inst_1))) s (fun (i : ι) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i)) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i))))
 Case conversion may be inaccurate. Consider using '#align lagrange.nodal_eq Lagrange.nodal_eqₓ'. -/
 theorem nodal_eq (s : Finset ι) (v : ι → F) : nodal s v = ∏ i in s, X - C (v i) :=
   rfl
@@ -771,7 +771,7 @@ theorem nodal_eq_mul_nodal_erase [DecidableEq ι] (hi : i ∈ s) :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {i : ι} (v : ι -> F), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Dvd.Dvd.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.commRing.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1))))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (v i))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {i : ι} (v : ι -> F), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Dvd.dvd.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1)))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i)) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {i : ι} (v : ι -> F), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Dvd.dvd.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.commRing.{u1} F (Field.toCommRing.{u1} F _inst_1)))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i)) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v))
 Case conversion may be inaccurate. Consider using '#align lagrange.X_sub_C_dvd_nodal Lagrange.X_sub_C_dvd_nodalₓ'. -/
 theorem X_sub_C_dvd_nodal (v : ι → F) (hi : i ∈ s) : X - C (v i) ∣ nodal s v :=
   ⟨_, by classical exact nodal_eq_mul_nodal_erase hi⟩
@@ -905,7 +905,7 @@ theorem eval_basis_not_at_node (hi : i ∈ s) (hxi : x ≠ v i) :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) [_inst_2 : DecidableEq.{succ u2} ι], Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (Finset.sum.{u1, u2} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) ι (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.hasDiv.{u1} F _inst_1)) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (v i))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (r i))))
 but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) [_inst_2 : DecidableEq.{succ u1} ι], Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (Finset.sum.{u2, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (NonAssocRing.toNonUnitalNonAssocRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Ring.toNonAssocRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (CommRing.toRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (EuclideanDomain.toCommRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (HDiv.hDiv.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHDiv.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instDivPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1)) (Lagrange.nodal.{u2, u1} F _inst_1 ι s v) (HSub.hSub.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (v i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHSub.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.sub.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (Polynomial.X.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (v i))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i))))
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) [_inst_2 : DecidableEq.{succ u1} ι], Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (Finset.sum.{u2, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (NonAssocRing.toNonUnitalNonAssocRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Ring.toNonAssocRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (CommRing.toRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (EuclideanDomain.toCommRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (HDiv.hDiv.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHDiv.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instDivPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1)) (Lagrange.nodal.{u2, u1} F _inst_1 ι s v) (HSub.hSub.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (v i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHSub.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.sub.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (Polynomial.X.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (v i))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i))))
 Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_nodal_weight_mul_nodal_div_X_sub_C Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_Cₓ'. -/
 theorem interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C :
     interpolate s v r = ∑ i in s, C (nodalWeight s v i) * (nodal s v / (X - C (v i))) * C (r i) :=
@@ -916,7 +916,7 @@ theorem interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) x (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) x (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)) (Finset.sum.{u1, u2} F ι (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (DivInvMonoid.toHasInv.{u1} F (DivisionRing.toDivInvMonoid.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toHasSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (AddGroupWithOne.toAddGroup.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))) x (v i)))) (r i)))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))) (r i)))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))) (r i)))))
 Case conversion may be inaccurate. Consider using '#align lagrange.eval_interpolate_not_at_node Lagrange.eval_interpolate_not_at_nodeₓ'. -/
 /-- This is the first barycentric form of the Lagrange interpolant. -/
 theorem eval_interpolate_not_at_node (hx : ∀ i ∈ s, x ≠ v i) :
@@ -945,7 +945,7 @@ theorem sum_nodalWeight_mul_inv_sub_ne_zero (hvs : Set.InjOn v s) (hx : ∀ i 
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Finset.Nonempty.{u2} ι s) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) x (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HDiv.hDiv.{u1, u1, u1} F F F (instHDiv.{u1} F (DivInvMonoid.toHasDiv.{u1} F (DivisionRing.toDivInvMonoid.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Finset.sum.{u1, u2} F ι (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (DivInvMonoid.toHasInv.{u1} F (DivisionRing.toDivInvMonoid.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toHasSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (AddGroupWithOne.toAddGroup.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))) x (v i)))) (r i))) (Finset.sum.{u1, u2} F ι (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (DivInvMonoid.toHasInv.{u1} F (DivisionRing.toDivInvMonoid.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toHasSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (AddGroupWithOne.toAddGroup.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))) x (v i)))))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Finset.Nonempty.{u2} ι s) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HDiv.hDiv.{u1, u1, u1} F F F (instHDiv.{u1} F (Field.toDiv.{u1} F _inst_1)) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))) (r i))) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Finset.Nonempty.{u2} ι s) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HDiv.hDiv.{u1, u1, u1} F F F (instHDiv.{u1} F (Field.toDiv.{u1} F _inst_1)) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))) (r i))) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))))))
 Case conversion may be inaccurate. Consider using '#align lagrange.eval_interpolate_not_at_node' Lagrange.eval_interpolate_not_at_node'ₓ'. -/
 /-- This is the second barycentric form of the Lagrange interpolant. -/
 theorem eval_interpolate_not_at_node' (hvs : Set.InjOn v s) (hs : s.Nonempty)

b5ad1414

bump to nightly-2023-05-08-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

508651e1

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Wrenna Robson
 
 ! This file was ported from Lean 3 source module linear_algebra.lagrange
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit b5ad141426bb005414324f89719c77c0aa3ec612
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.RingTheory.Polynomial.Basic
 /-!
 # Lagrange interpolation
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 ## Main definitions
 * In everything that follows, `s : finset ι` is a finite set of indexes, with `v : ι → F` an
 indexing of the field over some type. We call the image of v on s the interpolation nodes,

70fd9563

bump to nightly-2023-05-06-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/3905fa80e62c0898131285baab35559fbc4e5cda

c6fb1d2b

Diff

@@ -48,6 +48,12 @@ open Function Fintype
 
 variable (s : Finset R)
 
+/- warning: polynomial.eq_zero_of_degree_lt_of_eval_finset_eq_zero -> Polynomial.eq_zero_of_degree_lt_of_eval_finset_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} (s : Finset.{u1} R), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u1} R s))) -> (forall (x : R), (Membership.Mem.{u1, u1} R (Finset.{u1} R) (Finset.hasMem.{u1} R) x s) -> (Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x f) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} (s : Finset.{u1} R), (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} R s))) -> (forall (x : R), (Membership.mem.{u1, u1} R (Finset.{u1} R) (Finset.instMembershipFinset.{u1} R) x s) -> (Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x f) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.eq_zero_of_degree_lt_of_eval_finset_eq_zero Polynomial.eq_zero_of_degree_lt_of_eval_finset_eq_zeroₓ'. -/
 theorem eq_zero_of_degree_lt_of_eval_finset_eq_zero (degree_f_lt : f.degree < s.card)
     (eval_f : ∀ x ∈ s, f.eval x = 0) : f = 0 :=
   by
@@ -60,6 +66,7 @@ theorem eq_zero_of_degree_lt_of_eval_finset_eq_zero (degree_f_lt : f.degree < s.
       fun _ => eval_f _ (Finset.coe_mem _)
 #align polynomial.eq_zero_of_degree_lt_of_eval_finset_eq_zero Polynomial.eq_zero_of_degree_lt_of_eval_finset_eq_zero
 
+#print Polynomial.eq_of_degree_sub_lt_of_eval_finset_eq /-
 theorem eq_of_degree_sub_lt_of_eval_finset_eq (degree_fg_lt : (f - g).degree < s.card)
     (eval_fg : ∀ x ∈ s, f.eval x = g.eval x) : f = g :=
   by
@@ -68,7 +75,9 @@ theorem eq_of_degree_sub_lt_of_eval_finset_eq (degree_fg_lt : (f - g).degree < s
   simp_rw [eval_sub, sub_eq_zero]
   exact eval_fg
 #align polynomial.eq_of_degree_sub_lt_of_eval_finset_eq Polynomial.eq_of_degree_sub_lt_of_eval_finset_eq
+-/
 
+#print Polynomial.eq_of_degrees_lt_of_eval_finset_eq /-
 theorem eq_of_degrees_lt_of_eval_finset_eq (degree_f_lt : f.degree < s.card)
     (degree_g_lt : g.degree < s.card) (eval_fg : ∀ x ∈ s, f.eval x = g.eval x) : f = g :=
   by
@@ -76,6 +85,7 @@ theorem eq_of_degrees_lt_of_eval_finset_eq (degree_f_lt : f.degree < s.card)
   refine' eq_of_degree_sub_lt_of_eval_finset_eq _ _ eval_fg
   rw [← mem_degree_lt]; exact Submodule.sub_mem _ degree_f_lt degree_g_lt
 #align polynomial.eq_of_degrees_lt_of_eval_finset_eq Polynomial.eq_of_degrees_lt_of_eval_finset_eq
+-/
 
 end Finset
 
@@ -85,6 +95,12 @@ open Finset
 
 variable {ι : Type _} {v : ι → R} (s : Finset ι)
 
+/- warning: polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zero -> Polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {ι : Type.{u2}} {v : ι -> R} (s : Finset.{u2} ι), (Set.InjOn.{u2, u1} ι R v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s))) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (v i) f) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {ι : Type.{u2}} {v : ι -> R} (s : Finset.{u2} ι), (Set.InjOn.{u2, u1} ι R v (Finset.toSet.{u2} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u2} ι s))) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (v i) f) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zero Polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zeroₓ'. -/
 theorem eq_zero_of_degree_lt_of_eval_index_eq_zero (hvs : Set.InjOn v s)
     (degree_f_lt : f.degree < s.card) (eval_f : ∀ i ∈ s, f.eval (v i) = 0) : f = 0 := by
   classical
@@ -95,6 +111,7 @@ theorem eq_zero_of_degree_lt_of_eval_index_eq_zero (hvs : Set.InjOn v s)
     exact eval_f _ hj
 #align polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zero Polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zero
 
+#print Polynomial.eq_of_degree_sub_lt_of_eval_index_eq /-
 theorem eq_of_degree_sub_lt_of_eval_index_eq (hvs : Set.InjOn v s)
     (degree_fg_lt : (f - g).degree < s.card) (eval_fg : ∀ i ∈ s, f.eval (v i) = g.eval (v i)) :
     f = g := by
@@ -103,7 +120,9 @@ theorem eq_of_degree_sub_lt_of_eval_index_eq (hvs : Set.InjOn v s)
   simp_rw [eval_sub, sub_eq_zero]
   exact eval_fg
 #align polynomial.eq_of_degree_sub_lt_of_eval_index_eq Polynomial.eq_of_degree_sub_lt_of_eval_index_eq
+-/
 
+#print Polynomial.eq_of_degrees_lt_of_eval_index_eq /-
 theorem eq_of_degrees_lt_of_eval_index_eq (hvs : Set.InjOn v s) (degree_f_lt : f.degree < s.card)
     (degree_g_lt : g.degree < s.card) (eval_fg : ∀ i ∈ s, f.eval (v i) = g.eval (v i)) : f = g :=
   by
@@ -111,6 +130,7 @@ theorem eq_of_degrees_lt_of_eval_index_eq (hvs : Set.InjOn v s) (degree_f_lt : f
   rw [← mem_degree_lt] at degree_f_lt degree_g_lt⊢
   exact Submodule.sub_mem _ degree_f_lt degree_g_lt
 #align polynomial.eq_of_degrees_lt_of_eval_index_eq Polynomial.eq_of_degrees_lt_of_eval_index_eq
+-/
 
 end Indexed
 
@@ -130,57 +150,87 @@ section BasisDivisor
 
 variable {x y : F}
 
+#print Lagrange.basisDivisor /-
 /-- `basis_divisor x y` is the unique linear or constant polynomial such that
 when evaluated at `x` it gives `1` and `y` it gives `0` (where when `x = y` it is identically `0`).
 Such polynomials are the building blocks for the Lagrange interpolants. -/
 def basisDivisor (x y : F) : F[X] :=
   C (x - y)⁻¹ * (X - C y)
 #align lagrange.basis_divisor Lagrange.basisDivisor
+-/
 
+#print Lagrange.basisDivisor_self /-
 theorem basisDivisor_self : basisDivisor x x = 0 := by
   simp only [basis_divisor, sub_self, inv_zero, map_zero, MulZeroClass.zero_mul]
 #align lagrange.basis_divisor_self Lagrange.basisDivisor_self
+-/
 
+#print Lagrange.basisDivisor_inj /-
 theorem basisDivisor_inj (hxy : basisDivisor x y = 0) : x = y :=
   by
   simp_rw [basis_divisor, mul_eq_zero, X_sub_C_ne_zero, or_false_iff, C_eq_zero, inv_eq_zero,
     sub_eq_zero] at hxy
   exact hxy
 #align lagrange.basis_divisor_inj Lagrange.basisDivisor_inj
+-/
 
+#print Lagrange.basisDivisor_eq_zero_iff /-
 @[simp]
 theorem basisDivisor_eq_zero_iff : basisDivisor x y = 0 ↔ x = y :=
   ⟨basisDivisor_inj, fun H => H ▸ basisDivisor_self⟩
 #align lagrange.basis_divisor_eq_zero_iff Lagrange.basisDivisor_eq_zero_iff
+-/
 
+#print Lagrange.basisDivisor_ne_zero_iff /-
 theorem basisDivisor_ne_zero_iff : basisDivisor x y ≠ 0 ↔ x ≠ y := by
   rw [Ne.def, basis_divisor_eq_zero_iff]
 #align lagrange.basis_divisor_ne_zero_iff Lagrange.basisDivisor_ne_zero_iff
+-/
 
+#print Lagrange.degree_basisDivisor_of_ne /-
 theorem degree_basisDivisor_of_ne (hxy : x ≠ y) : (basisDivisor x y).degree = 1 :=
   by
   rw [basis_divisor, degree_mul, degree_X_sub_C, degree_C, zero_add]
   exact inv_ne_zero (sub_ne_zero_of_ne hxy)
 #align lagrange.degree_basis_divisor_of_ne Lagrange.degree_basisDivisor_of_ne
+-/
 
+#print Lagrange.degree_basisDivisor_self /-
 @[simp]
 theorem degree_basisDivisor_self : (basisDivisor x x).degree = ⊥ := by
   rw [basis_divisor_self, degree_zero]
 #align lagrange.degree_basis_divisor_self Lagrange.degree_basisDivisor_self
+-/
 
+#print Lagrange.natDegree_basisDivisor_self /-
 theorem natDegree_basisDivisor_self : (basisDivisor x x).natDegree = 0 := by
   rw [basis_divisor_self, nat_degree_zero]
 #align lagrange.nat_degree_basis_divisor_self Lagrange.natDegree_basisDivisor_self
+-/
 
+#print Lagrange.natDegree_basisDivisor_of_ne /-
 theorem natDegree_basisDivisor_of_ne (hxy : x ≠ y) : (basisDivisor x y).natDegree = 1 :=
   natDegree_eq_of_degree_eq_some (degree_basisDivisor_of_ne hxy)
 #align lagrange.nat_degree_basis_divisor_of_ne Lagrange.natDegree_basisDivisor_of_ne
+-/
 
+/- warning: lagrange.eval_basis_divisor_right -> Lagrange.eval_basisDivisor_right is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {x : F} {y : F}, Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) y (Lagrange.basisDivisor.{u1} F _inst_1 x y)) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))
+but is expected to have type
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {x : F} {y : F}, Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) y (Lagrange.basisDivisor.{u1} F _inst_1 x y)) (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (CommMonoidWithZero.toZero.{u1} F (CommGroupWithZero.toCommMonoidWithZero.{u1} F (Semifield.toCommGroupWithZero.{u1} F (Field.toSemifield.{u1} F _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align lagrange.eval_basis_divisor_right Lagrange.eval_basisDivisor_rightₓ'. -/
 @[simp]
 theorem eval_basisDivisor_right : eval y (basisDivisor x y) = 0 := by
   simp only [basis_divisor, eval_mul, eval_C, eval_sub, eval_X, sub_self, MulZeroClass.mul_zero]
 #align lagrange.eval_basis_divisor_right Lagrange.eval_basisDivisor_right
 
+/- warning: lagrange.eval_basis_divisor_left_of_ne -> Lagrange.eval_basisDivisor_left_of_ne is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {x : F} {y : F}, (Ne.{succ u1} F x y) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) x (Lagrange.basisDivisor.{u1} F _inst_1 x y)) (OfNat.ofNat.{u1} F 1 (OfNat.mk.{u1} F 1 (One.one.{u1} F (AddMonoidWithOne.toOne.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))
+but is expected to have type
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {x : F} {y : F}, (Ne.{succ u1} F x y) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (Lagrange.basisDivisor.{u1} F _inst_1 x y)) (OfNat.ofNat.{u1} F 1 (One.toOfNat1.{u1} F (NonAssocRing.toOne.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align lagrange.eval_basis_divisor_left_of_ne Lagrange.eval_basisDivisor_left_of_neₓ'. -/
 theorem eval_basisDivisor_left_of_ne (hxy : x ≠ y) : eval x (basisDivisor x y) = 1 :=
   by
   simp only [basis_divisor, eval_mul, eval_C, eval_sub, eval_X]
@@ -195,36 +245,55 @@ open Finset
 
 variable {ι : Type _} [DecidableEq ι] {s : Finset ι} {v : ι → F} {i j : ι}
 
+#print Lagrange.basis /-
 /-- Lagrange basis polynomials indexed by `s : finset ι`, defined at nodes `v i` for a
 map `v : ι → F`. For `i, j ∈ s`, `basis s v i` evaluates to 0 at `v j` for `i ≠ j`. When
 `v` is injective on `s`, `basis s v i` evaluates to 1 at `v i`. -/
 protected def basis (s : Finset ι) (v : ι → F) (i : ι) : F[X] :=
   ∏ j in s.eraseₓ i, basisDivisor (v i) (v j)
 #align lagrange.basis Lagrange.basis
+-/
 
+/- warning: lagrange.basis_empty -> Lagrange.basis_empty is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {v : ι -> F} {i : ι}, Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (EmptyCollection.emptyCollection.{u2} (Finset.{u2} ι) (Finset.hasEmptyc.{u2} ι)) v i) (OfNat.ofNat.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 1 (OfNat.mk.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 1 (One.one.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.hasOne.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))
+but is expected to have type
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {v : ι -> F} {i : ι}, Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.basis.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (EmptyCollection.emptyCollection.{u1} (Finset.{u1} ι) (Finset.instEmptyCollectionFinset.{u1} ι)) v i) (OfNat.ofNat.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) 1 (One.toOfNat1.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.one.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align lagrange.basis_empty Lagrange.basis_emptyₓ'. -/
 @[simp]
 theorem basis_empty : Lagrange.basis ∅ v i = 1 :=
   rfl
 #align lagrange.basis_empty Lagrange.basis_empty
 
+/- warning: lagrange.basis_singleton -> Lagrange.basis_singleton is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {v : ι -> F} (i : ι), Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Singleton.singleton.{u2, u2} ι (Finset.{u2} ι) (Finset.hasSingleton.{u2} ι) i) v i) (OfNat.ofNat.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 1 (OfNat.mk.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 1 (One.one.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.hasOne.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))
+but is expected to have type
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {v : ι -> F} (i : ι), Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.basis.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Singleton.singleton.{u1, u1} ι (Finset.{u1} ι) (Finset.instSingletonFinset.{u1} ι) i) v i) (OfNat.ofNat.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) 1 (One.toOfNat1.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.one.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align lagrange.basis_singleton Lagrange.basis_singletonₓ'. -/
 @[simp]
 theorem basis_singleton (i : ι) : Lagrange.basis {i} v i = 1 := by
   rw [Lagrange.basis, erase_singleton, prod_empty]
 #align lagrange.basis_singleton Lagrange.basis_singleton
 
+#print Lagrange.basis_pair_left /-
 @[simp]
 theorem basis_pair_left (hij : i ≠ j) : Lagrange.basis {i, j} v i = basisDivisor (v i) (v j) := by
   simp only [Lagrange.basis, hij, erase_insert_eq_erase, erase_eq_of_not_mem, mem_singleton,
     not_false_iff, prod_singleton]
 #align lagrange.basis_pair_left Lagrange.basis_pair_left
+-/
 
+#print Lagrange.basis_pair_right /-
 @[simp]
 theorem basis_pair_right (hij : i ≠ j) : Lagrange.basis {i, j} v j = basisDivisor (v j) (v i) :=
   by
   rw [pair_comm]
   exact basis_pair_left hij.symm
 #align lagrange.basis_pair_right Lagrange.basis_pair_right
+-/
 
+#print Lagrange.basis_ne_zero /-
 theorem basis_ne_zero (hvs : Set.InjOn v s) (hi : i ∈ s) : Lagrange.basis s v i ≠ 0 :=
   by
   simp_rw [Lagrange.basis, prod_ne_zero_iff, Ne.def, mem_erase]
@@ -232,7 +301,14 @@ theorem basis_ne_zero (hvs : Set.InjOn v s) (hi : i ∈ s) : Lagrange.basis s v
   rw [basis_divisor_eq_zero_iff, hvs.eq_iff hi hj]
   exact hij.symm
 #align lagrange.basis_ne_zero Lagrange.basis_ne_zero
+-/
 
+/- warning: lagrange.eval_basis_self -> Lagrange.eval_basis_self is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} {i : ι}, (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (OfNat.ofNat.{u1} F 1 (OfNat.mk.{u1} F 1 (One.one.{u1} F (AddMonoidWithOne.toOne.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))
+but is expected to have type
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} {i : ι}, (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (v i) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (OfNat.ofNat.{u1} F 1 (One.toOfNat1.{u1} F (NonAssocRing.toOne.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align lagrange.eval_basis_self Lagrange.eval_basis_selfₓ'. -/
 @[simp]
 theorem eval_basis_self (hvs : Set.InjOn v s) (hi : i ∈ s) :
     (Lagrange.basis s v i).eval (v i) = 1 :=
@@ -244,6 +320,12 @@ theorem eval_basis_self (hvs : Set.InjOn v s) (hi : i ∈ s) :
   exact mt (hvs hi hj) hij.symm
 #align lagrange.eval_basis_self Lagrange.eval_basis_self
 
+/- warning: lagrange.eval_basis_of_ne -> Lagrange.eval_basis_of_ne is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} {i : ι} {j : ι}, (Ne.{succ u2} ι i j) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) j s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v j) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))))))
+but is expected to have type
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} {i : ι} {j : ι}, (Ne.{succ u2} ι i j) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) j s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (v j) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (CommMonoidWithZero.toZero.{u1} F (CommGroupWithZero.toCommMonoidWithZero.{u1} F (Semifield.toCommGroupWithZero.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align lagrange.eval_basis_of_ne Lagrange.eval_basis_of_neₓ'. -/
 @[simp]
 theorem eval_basis_of_ne (hij : i ≠ j) (hj : j ∈ s) : (Lagrange.basis s v i).eval (v j) = 0 :=
   by
@@ -251,6 +333,7 @@ theorem eval_basis_of_ne (hij : i ≠ j) (hj : j ∈ s) : (Lagrange.basis s v i)
   exact ⟨j, ⟨mem_erase.mpr ⟨hij.symm, hj⟩, eval_basis_divisor_right⟩⟩
 #align lagrange.eval_basis_of_ne Lagrange.eval_basis_of_ne
 
+#print Lagrange.natDegree_basis /-
 @[simp]
 theorem natDegree_basis (hvs : Set.InjOn v s) (hi : i ∈ s) :
     (Lagrange.basis s v i).natDegree = s.card - 1 :=
@@ -265,12 +348,16 @@ theorem natDegree_basis (hvs : Set.InjOn v s) (hi : i ∈ s) :
   rw [Ne.def, ← basis_divisor_eq_zero_iff]
   exact H _ hj
 #align lagrange.nat_degree_basis Lagrange.natDegree_basis
+-/
 
+#print Lagrange.degree_basis /-
 theorem degree_basis (hvs : Set.InjOn v s) (hi : i ∈ s) :
     (Lagrange.basis s v i).degree = ↑(s.card - 1) := by
   rw [degree_eq_nat_degree (basis_ne_zero hvs hi), nat_degree_basis hvs hi]
 #align lagrange.degree_basis Lagrange.degree_basis
+-/
 
+#print Lagrange.sum_basis /-
 theorem sum_basis (hvs : Set.InjOn v s) (hs : s.Nonempty) : (∑ j in s, Lagrange.basis s v j) = 1 :=
   by
   refine' eq_of_degrees_lt_of_eval_index_eq s hvs (lt_of_le_of_lt (degree_sum_le _ _) _) _ _
@@ -287,7 +374,9 @@ theorem sum_basis (hvs : Set.InjOn v s) (hs : s.Nonempty) : (∑ j in s, Lagrang
     rcases mem_erase.mp hj with ⟨hij, hj⟩
     rw [eval_basis_of_ne hij hi]
 #align lagrange.sum_basis Lagrange.sum_basis
+-/
 
+#print Lagrange.basisDivisor_add_symm /-
 theorem basisDivisor_add_symm {x y : F} (hxy : x ≠ y) : basisDivisor x y + basisDivisor y x = 1 :=
   by
   classical rw [←
@@ -295,6 +384,7 @@ theorem basisDivisor_add_symm {x y : F} (hxy : x ≠ y) : basisDivisor x y + bas
       sum_insert (not_mem_singleton.mpr hxy), sum_singleton, basis_pair_left hxy,
       basis_pair_right hxy, id, id]
 #align lagrange.basis_divisor_add_symm Lagrange.basisDivisor_add_symm
+-/
 
 end Basis
 
@@ -304,6 +394,7 @@ open Finset
 
 variable {ι : Type _} [DecidableEq ι] {s t : Finset ι} {i j : ι} {v : ι → F} (r r' : ι → F)
 
+#print Lagrange.interpolate /-
 /-- Lagrange interpolation: given a finset `s : finset ι`, a nodal map  `v : ι → F` injective on
 `s` and a value function `r : ι → F`,  `interpolate s v r` is the unique
 polynomial of degree `< s.card` that takes value `r i` on `v i` for all `i` in `s`. -/
@@ -315,22 +406,47 @@ def interpolate (s : Finset ι) (v : ι → F) : (ι → F) →ₗ[F] F[X]
   map_smul' c f := by
     simp_rw [Finset.smul_sum, C_mul', smul_smul, Pi.smul_apply, RingHom.id_apply, smul_eq_mul]
 #align lagrange.interpolate Lagrange.interpolate
+-/
 
+/- warning: lagrange.interpolate_empty -> Lagrange.interpolate_empty is a dubious translation:
+lean 3 declaration is
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_inst_1)))) (Polynomial.zero.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))
+but is expected to have type
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(Finset.instEmptyCollectionFinset.{u1} ι)) v) r) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Polynomial.zero.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_empty Lagrange.interpolate_emptyₓ'. -/
 @[simp]
 theorem interpolate_empty : interpolate ∅ v r = 0 := by rw [interpolate_apply, sum_empty]
 #align lagrange.interpolate_empty Lagrange.interpolate_empty
 
+/- warning: lagrange.interpolate_singleton -> Lagrange.interpolate_singleton is a dubious translation:
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_inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Singleton.singleton.{u2, u2} ι (Finset.{u2} ι) (Finset.hasSingleton.{u2} ι) i) v) r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (r i))
+but is expected to have type
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {i : ι} {v : ι -> F} (r : ι -> F), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Singleton.singleton.{u1, u1} ι (Finset.{u1} ι) (Finset.instSingletonFinset.{u1} ι) i) v) r) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F 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_inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i))
+Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_singleton Lagrange.interpolate_singletonₓ'. -/
 @[simp]
 theorem interpolate_singleton : interpolate {i} v r = C (r i) := by
   rw [interpolate_apply, sum_singleton, basis_singleton, mul_one]
 #align lagrange.interpolate_singleton Lagrange.interpolate_singleton
 
+/- warning: lagrange.interpolate_one -> Lagrange.interpolate_one is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_one Lagrange.interpolate_oneₓ'. -/
 theorem interpolate_one (hvs : Set.InjOn v s) (hs : s.Nonempty) : interpolate s v 1 = 1 :=
   by
   simp_rw [interpolate_apply, Pi.one_apply, map_one, one_mul]
   exact sum_basis hvs hs
 #align lagrange.interpolate_one Lagrange.interpolate_one
 
+/- warning: lagrange.eval_interpolate_at_node -> Lagrange.eval_interpolate_at_node is a dubious translation:
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(NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (r i))
+Case conversion may be inaccurate. Consider using '#align lagrange.eval_interpolate_at_node Lagrange.eval_interpolate_at_nodeₓ'. -/
 theorem eval_interpolate_at_node (hvs : Set.InjOn v s) (hi : i ∈ s) :
     eval (v i) (interpolate s v r) = r i :=
   by
@@ -340,6 +456,12 @@ theorem eval_interpolate_at_node (hvs : Set.InjOn v s) (hi : i ∈ s) :
   rw [eval_basis_of_ne (mem_erase.mp H).1 hi, MulZeroClass.mul_zero]
 #align lagrange.eval_interpolate_at_node Lagrange.eval_interpolate_at_node
 
+/- warning: lagrange.degree_interpolate_le -> Lagrange.degree_interpolate_le is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align lagrange.degree_interpolate_le Lagrange.degree_interpolate_leₓ'. -/
 theorem degree_interpolate_le (hvs : Set.InjOn v s) : (interpolate s v r).degree ≤ ↑(s.card - 1) :=
   by
   refine' (degree_sum_le _ _).trans _
@@ -351,6 +473,12 @@ theorem degree_interpolate_le (hvs : Set.InjOn v s) : (interpolate s v r).degree
   · rw [degree_C hr, zero_add, WithBot.coe_le_coe]
 #align lagrange.degree_interpolate_le Lagrange.degree_interpolate_le
 
+/- warning: lagrange.degree_interpolate_lt -> Lagrange.degree_interpolate_lt is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align lagrange.degree_interpolate_lt Lagrange.degree_interpolate_ltₓ'. -/
 theorem degree_interpolate_lt (hvs : Set.InjOn v s) : (interpolate s v r).degree < s.card :=
   by
   rcases eq_empty_or_nonempty s with (rfl | h)
@@ -361,6 +489,12 @@ theorem degree_interpolate_lt (hvs : Set.InjOn v s) : (interpolate s v r).degree
     exact Nat.sub_lt (nonempty.card_pos h) zero_lt_one
 #align lagrange.degree_interpolate_lt Lagrange.degree_interpolate_lt
 
+/- warning: lagrange.degree_interpolate_erase_lt -> Lagrange.degree_interpolate_erase_lt is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align lagrange.degree_interpolate_erase_lt Lagrange.degree_interpolate_erase_ltₓ'. -/
 theorem degree_interpolate_erase_lt (hvs : Set.InjOn v s) (hi : i ∈ s) :
     (interpolate (s.eraseₓ i) v r).degree < ↑(s.card - 1) :=
   by
@@ -368,27 +502,57 @@ theorem degree_interpolate_erase_lt (hvs : Set.InjOn v s) (hi : i ∈ s) :
   exact degree_interpolate_lt _ (Set.InjOn.mono (coe_subset.mpr (erase_subset _ _)) hvs)
 #align lagrange.degree_interpolate_erase_lt Lagrange.degree_interpolate_erase_lt
 
+/- warning: lagrange.values_eq_on_of_interpolate_eq -> Lagrange.values_eq_on_of_interpolate_eq is a dubious translation:
+lean 3 declaration is
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(Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i)))
+but is expected to have type
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) (r' : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F 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(DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) 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(Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F 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+Case conversion may be inaccurate. Consider using '#align lagrange.values_eq_on_of_interpolate_eq Lagrange.values_eq_on_of_interpolate_eqₓ'. -/
 theorem values_eq_on_of_interpolate_eq (hvs : Set.InjOn v s)
     (hrr' : interpolate s v r = interpolate s v r') : ∀ i ∈ s, r i = r' i := fun _ hi => by
   rw [← eval_interpolate_at_node r hvs hi, hrr', eval_interpolate_at_node r' hvs hi]
 #align lagrange.values_eq_on_of_interpolate_eq Lagrange.values_eq_on_of_interpolate_eq
 
+/- warning: lagrange.interpolate_eq_of_values_eq_on -> Lagrange.interpolate_eq_of_values_eq_on is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_of_values_eq_on Lagrange.interpolate_eq_of_values_eq_onₓ'. -/
 theorem interpolate_eq_of_values_eq_on (hrr' : ∀ i ∈ s, r i = r' i) :
     interpolate s v r = interpolate s v r' :=
   sum_congr rfl fun i hi => by rw [hrr' _ hi]
 #align lagrange.interpolate_eq_of_values_eq_on Lagrange.interpolate_eq_of_values_eq_on
 
+/- warning: lagrange.interpolate_eq_iff_values_eq_on -> Lagrange.interpolate_eq_iff_values_eq_on is a dubious translation:
+lean 3 declaration is
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(Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} 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(Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r')) (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (r i) (r' i))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_iff_values_eq_on Lagrange.interpolate_eq_iff_values_eq_onₓ'. -/
 theorem interpolate_eq_iff_values_eq_on (hvs : Set.InjOn v s) :
     interpolate s v r = interpolate s v r' ↔ ∀ i ∈ s, r i = r' i :=
   ⟨values_eq_on_of_interpolate_eq _ _ hvs, interpolate_eq_of_values_eq_on _ _⟩
 #align lagrange.interpolate_eq_iff_values_eq_on Lagrange.interpolate_eq_iff_values_eq_on
 
+/- warning: lagrange.eq_interpolate -> Lagrange.eq_interpolate is a dubious translation:
+lean 3 declaration is
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(NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F 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+but is expected to have type
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) -> (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F 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(Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F 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: ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) (fun (i : ι) => Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f)))
+Case conversion may be inaccurate. Consider using '#align lagrange.eq_interpolate Lagrange.eq_interpolateₓ'. -/
 theorem eq_interpolate {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree < s.card) :
     f = interpolate s v fun i => f.eval (v i) :=
   eq_of_degrees_lt_of_eval_index_eq _ hvs degree_f_lt (degree_interpolate_lt _ hvs) fun i hi =>
     (eval_interpolate_at_node _ hvs hi).symm
 #align lagrange.eq_interpolate Lagrange.eq_interpolate
 
+/- warning: lagrange.eq_interpolate_of_eval_eq -> Lagrange.eq_interpolate_of_eval_eq is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (Finset.card.{u2} ι s))) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) f) (r i))) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F 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(DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r))
+but is expected to have type
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (Finset.card.{u1} ι s))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u2} F (Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) f) (r i))) -> (Eq.{succ u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) 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_inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r))
+Case conversion may be inaccurate. Consider using '#align lagrange.eq_interpolate_of_eval_eq Lagrange.eq_interpolate_of_eval_eqₓ'. -/
 theorem eq_interpolate_of_eval_eq {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree < s.card)
     (eval_f : ∀ i ∈ s, f.eval (v i) = r i) : f = interpolate s v r :=
   by
@@ -396,6 +560,12 @@ theorem eq_interpolate_of_eval_eq {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt
   exact interpolate_eq_of_values_eq_on _ _ eval_f
 #align lagrange.eq_interpolate_of_eval_eq Lagrange.eq_interpolate_of_eval_eq
 
+/- warning: lagrange.eq_interpolate_iff -> Lagrange.eq_interpolate_iff is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Iff (And (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) f) ((fun (a : Type) (b : Type) [self 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+but is expected to have type
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_2 : DecidableEq.{succ u1} ι] {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) {f : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))}, (Set.InjOn.{u1, u2} ι F v (Finset.toSet.{u1} ι s)) -> (Iff (And (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring 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_inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)))
+Case conversion may be inaccurate. Consider using '#align lagrange.eq_interpolate_iff Lagrange.eq_interpolate_iffₓ'. -/
 /-- This is the characteristic property of the interpolation: the interpolation is the
 unique polynomial of `degree < fintype.card ι` which takes the value of the `r i` on the `v i`.
 -/
@@ -408,9 +578,10 @@ theorem eq_interpolate_iff {f : F[X]} (hvs : Set.InjOn v s) :
     exact ⟨degree_interpolate_lt _ hvs, fun _ hi => eval_interpolate_at_node _ hvs hi⟩
 #align lagrange.eq_interpolate_iff Lagrange.eq_interpolate_iff
 
+#print Lagrange.funEquivDegreeLT /-
 /-- Lagrange interpolation induces isomorphism between functions from `s`
 and polynomials of degree less than `fintype.card ι`.-/
-def funEquivDegreeLt (hvs : Set.InjOn v s) : degreeLT F s.card ≃ₗ[F] s → F
+def funEquivDegreeLT (hvs : Set.InjOn v s) : degreeLT F s.card ≃ₗ[F] s → F
     where
   toFun f i := f.1.eval (v i)
   map_add' f g := funext fun v => eval_add
@@ -429,8 +600,15 @@ def funEquivDegreeLt (hvs : Set.InjOn v s) : degreeLT F s.card ≃ₗ[F] s → F
     ext ⟨i, hi⟩
     simp only [Subtype.coe_mk, eval_interpolate_at_node _ hvs hi]
     exact dif_pos hi
-#align lagrange.fun_equiv_degree_lt Lagrange.funEquivDegreeLt
+#align lagrange.fun_equiv_degree_lt Lagrange.funEquivDegreeLT
+-/
 
+/- warning: lagrange.interpolate_eq_sum_interpolate_insert_sdiff -> Lagrange.interpolate_eq_sum_interpolate_insert_sdiff is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {t : Finset.{u2} ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) t)) -> (Finset.Nonempty.{u2} ι s) -> (HasSubset.Subset.{u2} (Finset.{u2} ι) (Finset.hasSubset.{u2} ι) s t) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) t v) r) (Finset.sum.{u1, u2} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) ι (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Insert.insert.{u2, u2} ι (Finset.{u2} ι) (Finset.hasInsert.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) i (SDiff.sdiff.{u2} (Finset.{u2} ι) (Finset.hasSdiff.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) t s)) v) r) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i))))
+but is expected to have type
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HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max 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F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Insert.insert.{u2, u2} ι (Finset.{u2} ι) (Finset.instInsertFinset.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) i (SDiff.sdiff.{u2} (Finset.{u2} ι) (Finset.instSDiffFinset.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b)) t s)) v) r) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i))))
+Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_sum_interpolate_insert_sdiff Lagrange.interpolate_eq_sum_interpolate_insert_sdiffₓ'. -/
 theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs : s.Nonempty)
     (hst : s ⊆ t) :
     interpolate t v r = ∑ i in s, interpolate (insert i (t \ s)) v r * Lagrange.basis s v i :=
@@ -469,6 +647,12 @@ theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs :
           (mem_insert.mpr (Or.inr (mem_sdiff.mpr ⟨hi, hi'⟩)))
 #align lagrange.interpolate_eq_sum_interpolate_insert_sdiff Lagrange.interpolate_eq_sum_interpolate_insert_sdiff
 
+/- warning: lagrange.interpolate_eq_add_interpolate_erase -> Lagrange.interpolate_eq_add_interpolate_erase is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {j : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) j s) -> (Ne.{succ u2} ι i j) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHAdd.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.add'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s j) v) r) (Lagrange.basisDivisor.{u1} F _inst_1 (v i) (v j))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (LinearMap.{u1, u1, max u2 u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} 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(DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (ι -> F) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u1} F F (ι -> F) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => F) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Pi.Function.module.{u2, u1, u1} ι F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v) r) (Lagrange.basisDivisor.{u1} F _inst_1 (v j) (v i)))))
+but is expected to have type
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] {s : Finset.{u2} ι} {i : ι} {j : ι} {v : ι -> F} (r : ι -> F), (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) j s) -> (Ne.{succ u2} ι i j) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) r) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u1} F F (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Pi.addCommMonoid.{u2, 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+Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_add_interpolate_erase Lagrange.interpolate_eq_add_interpolate_eraseₓ'. -/
 theorem interpolate_eq_add_interpolate_erase (hvs : Set.InjOn v s) (hi : i ∈ s) (hj : j ∈ s)
     (hij : i ≠ j) :
     interpolate s v r =
@@ -492,6 +676,7 @@ open Finset Polynomial
 
 variable {ι : Type _} {s : Finset ι} {v : ι → F} {i : ι} (r : ι → F) {x : F}
 
+#print Lagrange.nodal /-
 /-- `nodal s v` is the unique monic polynomial whose roots are the nodes defined by `v` and `s`.
 
 That is, the roots of `nodal s v` are exactly the image of `v` on `s`,
@@ -502,56 +687,123 @@ We can use `nodal` to define the barycentric forms of the evaluated interpolant.
 def nodal (s : Finset ι) (v : ι → F) : F[X] :=
   ∏ i in s, X - C (v i)
 #align lagrange.nodal Lagrange.nodal
+-/
 
+/- warning: lagrange.nodal_eq -> Lagrange.nodal_eq is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align lagrange.nodal_eq Lagrange.nodal_eqₓ'. -/
 theorem nodal_eq (s : Finset ι) (v : ι → F) : nodal s v = ∏ i in s, X - C (v i) :=
   rfl
 #align lagrange.nodal_eq Lagrange.nodal_eq
 
+/- warning: lagrange.nodal_empty -> Lagrange.nodal_empty is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align lagrange.nodal_empty Lagrange.nodal_emptyₓ'. -/
 @[simp]
 theorem nodal_empty : nodal ∅ v = 1 :=
   rfl
 #align lagrange.nodal_empty Lagrange.nodal_empty
 
+/- warning: lagrange.degree_nodal -> Lagrange.degree_nodal is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align lagrange.degree_nodal Lagrange.degree_nodalₓ'. -/
 theorem degree_nodal : (nodal s v).degree = s.card := by
   simp_rw [nodal, degree_prod, degree_X_sub_C, sum_const, Nat.smul_one_eq_coe]
 #align lagrange.degree_nodal Lagrange.degree_nodal
 
+/- warning: lagrange.eval_nodal -> Lagrange.eval_nodal is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align lagrange.eval_nodal Lagrange.eval_nodalₓ'. -/
 theorem eval_nodal {x : F} : (nodal s v).eval x = ∏ i in s, x - v i := by
   simp_rw [nodal, eval_prod, eval_sub, eval_X, eval_C]
 #align lagrange.eval_nodal Lagrange.eval_nodal
 
+/- warning: lagrange.eval_nodal_at_node -> Lagrange.eval_nodal_at_node is a dubious translation:
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+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι}, (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (v i) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)) (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (CommMonoidWithZero.toZero.{u1} F (CommGroupWithZero.toCommMonoidWithZero.{u1} F (Semifield.toCommGroupWithZero.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align lagrange.eval_nodal_at_node Lagrange.eval_nodal_at_nodeₓ'. -/
 theorem eval_nodal_at_node (hi : i ∈ s) : eval (v i) (nodal s v) = 0 :=
   by
   rw [eval_nodal, prod_eq_zero_iff]
   exact ⟨i, hi, sub_eq_zero_of_eq rfl⟩
 #align lagrange.eval_nodal_at_node Lagrange.eval_nodal_at_node
 
+/- warning: lagrange.eval_nodal_not_at_node -> Lagrange.eval_nodal_not_at_node is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align lagrange.eval_nodal_not_at_node Lagrange.eval_nodal_not_at_nodeₓ'. -/
 theorem eval_nodal_not_at_node (hx : ∀ i ∈ s, x ≠ v i) : eval x (nodal s v) ≠ 0 :=
   by
   simp_rw [nodal, eval_prod, prod_ne_zero_iff, eval_sub, eval_X, eval_C, sub_ne_zero]
   exact hx
 #align lagrange.eval_nodal_not_at_node Lagrange.eval_nodal_not_at_node
 
+/- warning: lagrange.nodal_eq_mul_nodal_erase -> Lagrange.nodal_eq_mul_nodal_erase is a dubious translation:
+lean 3 declaration is
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_inst_1)))) (v i))) (Lagrange.nodal.{u1, u2} F _inst_1 ι (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v)))
+Case conversion may be inaccurate. Consider using '#align lagrange.nodal_eq_mul_nodal_erase Lagrange.nodal_eq_mul_nodal_eraseₓ'. -/
 theorem nodal_eq_mul_nodal_erase [DecidableEq ι] (hi : i ∈ s) :
     nodal s v = (X - C (v i)) * nodal (s.eraseₓ i) v := by simp_rw [nodal, mul_prod_erase _ _ hi]
 #align lagrange.nodal_eq_mul_nodal_erase Lagrange.nodal_eq_mul_nodal_erase
 
-theorem x_sub_c_dvd_nodal (v : ι → F) (hi : i ∈ s) : X - C (v i) ∣ nodal s v :=
+/- warning: lagrange.X_sub_C_dvd_nodal -> Lagrange.X_sub_C_dvd_nodal is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {i : ι} (v : ι -> F), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Dvd.Dvd.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.commRing.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1))))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (v i))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v))
+but is expected to have type
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_inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) 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+Case conversion may be inaccurate. Consider using '#align lagrange.X_sub_C_dvd_nodal Lagrange.X_sub_C_dvd_nodalₓ'. -/
+theorem X_sub_C_dvd_nodal (v : ι → F) (hi : i ∈ s) : X - C (v i) ∣ nodal s v :=
   ⟨_, by classical exact nodal_eq_mul_nodal_erase hi⟩
-#align lagrange.X_sub_C_dvd_nodal Lagrange.x_sub_c_dvd_nodal
+#align lagrange.X_sub_C_dvd_nodal Lagrange.X_sub_C_dvd_nodal
 
 variable [DecidableEq ι]
 
+/- warning: lagrange.nodal_erase_eq_nodal_div -> Lagrange.nodal_erase_eq_nodal_div is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i)))))
+Case conversion may be inaccurate. Consider using '#align lagrange.nodal_erase_eq_nodal_div Lagrange.nodal_erase_eq_nodal_divₓ'. -/
 theorem nodal_erase_eq_nodal_div (hi : i ∈ s) : nodal (s.eraseₓ i) v = nodal s v / (X - C (v i)) :=
   by
   rw [nodal_eq_mul_nodal_erase hi, EuclideanDomain.mul_div_cancel_left]
   exact X_sub_C_ne_zero _
 #align lagrange.nodal_erase_eq_nodal_div Lagrange.nodal_erase_eq_nodal_div
 
+/- warning: lagrange.nodal_insert_eq_nodal -> Lagrange.nodal_insert_eq_nodal is a dubious translation:
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+but is expected to have type
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(DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i)) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)))
+Case conversion may be inaccurate. Consider using '#align lagrange.nodal_insert_eq_nodal Lagrange.nodal_insert_eq_nodalₓ'. -/
 theorem nodal_insert_eq_nodal (hi : i ∉ s) : nodal (insert i s) v = (X - C (v i)) * nodal s v := by
   simp_rw [nodal, prod_insert hi]
 #align lagrange.nodal_insert_eq_nodal Lagrange.nodal_insert_eq_nodal
 
+/- warning: lagrange.derivative_nodal -> Lagrange.derivative_nodal is a dubious translation:
+lean 3 declaration is
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(Field.toDivisionRing.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)) (Finset.sum.{u1, u2} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) ι (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) s (fun (i : ι) => Lagrange.nodal.{u1, u2} F _inst_1 ι (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v))
+but is expected to have type
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} {s : Finset.{u1} ι} {v : ι -> F} [_inst_2 : DecidableEq.{succ u1} ι], Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodal.{u2, u1} F _inst_1 ι s v)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (fun (_x : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} F F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (Polynomial.derivative.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodal.{u2, u1} F _inst_1 ι s v)) (Finset.sum.{u2, u1} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Ring.toNonAssocRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (CommRing.toRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) s (fun (i : ι) => Lagrange.nodal.{u2, u1} F _inst_1 ι (Finset.erase.{u1} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v))
+Case conversion may be inaccurate. Consider using '#align lagrange.derivative_nodal Lagrange.derivative_nodalₓ'. -/
 theorem derivative_nodal : (nodal s v).derivative = ∑ i in s, nodal (s.eraseₓ i) v :=
   by
   refine' Finset.induction_on s _ fun _ _ hit IH => _
@@ -563,6 +815,12 @@ theorem derivative_nodal : (nodal s v).derivative = ∑ i in s, nodal (s.erase
       EuclideanDomain.mul_div_assoc _ (X_sub_C_dvd_nodal v hjt), nodal_erase_eq_nodal_div hjt]
 #align lagrange.derivative_nodal Lagrange.derivative_nodal
 
+/- warning: lagrange.eval_nodal_derivative_eval_node_eq -> Lagrange.eval_nodal_derivative_eval_node_eq is a dubious translation:
+lean 3 declaration is
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(DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.derivative.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v))) (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) (Lagrange.nodal.{u1, u2} F _inst_1 ι (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v)))
+but is expected to have type
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(Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} F F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F 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(DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F 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(Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (v i) (Lagrange.nodal.{u1, u2} F _inst_1 ι (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v)))
+Case conversion may be inaccurate. Consider using '#align lagrange.eval_nodal_derivative_eval_node_eq Lagrange.eval_nodal_derivative_eval_node_eqₓ'. -/
 theorem eval_nodal_derivative_eval_node_eq (hi : i ∈ s) :
     eval (v i) (nodal s v).derivative = eval (v i) (nodal (s.eraseₓ i) v) :=
   by
@@ -572,21 +830,41 @@ theorem eval_nodal_derivative_eval_node_eq (hi : i ∈ s) :
   exact ⟨i, ⟨(mem_erase.mp hj).1.symm, hi⟩, sub_eq_zero_of_eq rfl⟩
 #align lagrange.eval_nodal_derivative_eval_node_eq Lagrange.eval_nodal_derivative_eval_node_eq
 
+#print Lagrange.nodalWeight /-
 /-- This defines the nodal weight for a given set of node indexes and node mapping function `v`. -/
 def nodalWeight (s : Finset ι) (v : ι → F) (i : ι) :=
   ∏ j in s.eraseₓ i, (v i - v j)⁻¹
 #align lagrange.nodal_weight Lagrange.nodalWeight
+-/
 
+/- warning: lagrange.nodal_weight_eq_eval_nodal_erase_inv -> Lagrange.nodalWeight_eq_eval_nodal_erase_inv is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u2} ι], Eq.{succ u1} F (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (DivInvMonoid.toHasInv.{u1} F (DivisionRing.toDivInvMonoid.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (v i) (Lagrange.nodal.{u1, u2} F _inst_1 ι (Finset.erase.{u2} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v)))
+but is expected to have type
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} {s : Finset.{u1} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u1} ι], Eq.{succ u2} F (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u2} F (Field.toInv.{u2} F _inst_1) (Polynomial.eval.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (v i) (Lagrange.nodal.{u2, u1} F _inst_1 ι (Finset.erase.{u1} ι (fun (a : ι) (b : ι) => _inst_2 a b) s i) v)))
+Case conversion may be inaccurate. Consider using '#align lagrange.nodal_weight_eq_eval_nodal_erase_inv Lagrange.nodalWeight_eq_eval_nodal_erase_invₓ'. -/
 theorem nodalWeight_eq_eval_nodal_erase_inv :
     nodalWeight s v i = (eval (v i) (nodal (s.eraseₓ i) v))⁻¹ := by
   rw [eval_nodal, nodal_weight, prod_inv_distrib]
 #align lagrange.nodal_weight_eq_eval_nodal_erase_inv Lagrange.nodalWeight_eq_eval_nodal_erase_inv
 
+/- warning: lagrange.nodal_weight_eq_eval_nodal_derative -> Lagrange.nodalWeight_eq_eval_nodal_derative is a dubious translation:
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(Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F 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(Lagrange.nodal.{u1, u2} F _inst_1 ι s v)))))
+Case conversion may be inaccurate. Consider using '#align lagrange.nodal_weight_eq_eval_nodal_derative Lagrange.nodalWeight_eq_eval_nodal_derativeₓ'. -/
 theorem nodalWeight_eq_eval_nodal_derative (hi : i ∈ s) :
     nodalWeight s v i = (eval (v i) (nodal s v).derivative)⁻¹ := by
   rw [eval_nodal_derivative_eval_node_eq hi, nodal_weight_eq_eval_nodal_erase_inv]
 #align lagrange.nodal_weight_eq_eval_nodal_derative Lagrange.nodalWeight_eq_eval_nodal_derative
 
+/- warning: lagrange.nodal_weight_ne_zero -> Lagrange.nodalWeight_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u2} ι], (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Ne.{succ u1} F (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))))))
+but is expected to have type
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u2} ι], (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Ne.{succ u1} F (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (CommMonoidWithZero.toZero.{u1} F (CommGroupWithZero.toCommMonoidWithZero.{u1} F (Semifield.toCommGroupWithZero.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align lagrange.nodal_weight_ne_zero Lagrange.nodalWeight_ne_zeroₓ'. -/
 theorem nodalWeight_ne_zero (hvs : Set.InjOn v s) (hi : i ∈ s) : nodalWeight s v i ≠ 0 :=
   by
   rw [nodal_weight, prod_ne_zero_iff]
@@ -595,12 +873,24 @@ theorem nodalWeight_ne_zero (hvs : Set.InjOn v s) (hi : i ∈ s) : nodalWeight s
   refine' inv_ne_zero (sub_ne_zero_of_ne (mt (hvs.eq_iff hi hj).mp hij.symm))
 #align lagrange.nodal_weight_ne_zero Lagrange.nodalWeight_ne_zero
 
+/- warning: lagrange.basis_eq_prod_sub_inv_mul_nodal_div -> Lagrange.basis_eq_prod_sub_inv_mul_nodal_div is a dubious translation:
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F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.hasDiv.{u1} F _inst_1)) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (v i))))))
+but is expected to have type
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} [_inst_2 : DecidableEq.{succ u2} ι], (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.instDivPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_1)) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i)) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F 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(Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (v i))))))
+Case conversion may be inaccurate. Consider using '#align lagrange.basis_eq_prod_sub_inv_mul_nodal_div Lagrange.basis_eq_prod_sub_inv_mul_nodal_divₓ'. -/
 theorem basis_eq_prod_sub_inv_mul_nodal_div (hi : i ∈ s) :
     Lagrange.basis s v i = C (nodalWeight s v i) * (nodal s v / (X - C (v i))) := by
   simp_rw [Lagrange.basis, basis_divisor, nodal_weight, prod_mul_distrib, map_prod, ←
     nodal_erase_eq_nodal_div hi, nodal]
 #align lagrange.basis_eq_prod_sub_inv_mul_nodal_div Lagrange.basis_eq_prod_sub_inv_mul_nodal_div
 
+/- warning: lagrange.eval_basis_not_at_node -> Lagrange.eval_basis_not_at_node is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {i : ι} {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Ne.{succ u1} F x (v i)) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) x (Lagrange.basis.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) x (Lagrange.nodal.{u1, u2} F _inst_1 ι s v)) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (DivInvMonoid.toHasInv.{u1} F (DivisionRing.toDivInvMonoid.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toHasSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (AddGroupWithOne.toAddGroup.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))) x (v i))))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align lagrange.eval_basis_not_at_node Lagrange.eval_basis_not_at_nodeₓ'. -/
 theorem eval_basis_not_at_node (hi : i ∈ s) (hxi : x ≠ v i) :
     eval x (Lagrange.basis s v i) = eval x (nodal s v) * (nodalWeight s v i * (x - v i)⁻¹) := by
   rw [mul_comm, basis_eq_prod_sub_inv_mul_nodal_div hi, eval_mul, eval_C, ←
@@ -608,11 +898,23 @@ theorem eval_basis_not_at_node (hi : i ∈ s) (hxi : x ≠ v i) :
     mul_assoc (x - v i)⁻¹, inv_mul_cancel (sub_ne_zero_of_ne hxi), one_mul]
 #align lagrange.eval_basis_not_at_node Lagrange.eval_basis_not_at_node
 
-theorem interpolate_eq_nodalWeight_mul_nodal_div_x_sub_c :
+/- warning: lagrange.interpolate_eq_nodal_weight_mul_nodal_div_X_sub_C -> Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C is a dubious translation:
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(NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F 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(Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (HDiv.hDiv.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHDiv.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.hasDiv.{u1} F _inst_1)) (Lagrange.nodal.{u1, u2} F _inst_1 ι s v) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (v i))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (r i))))
+but is expected to have type
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} {s : Finset.{u1} ι} {v : ι -> F} (r : ι -> F) [_inst_2 : DecidableEq.{succ u1} ι], Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (LinearMap.{u2, u2, max u2 u1, u2} F F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (RingHom.id.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))) (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (ι -> F) (fun (_x : ι -> F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u2} F F (ι -> F) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => F) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonUnitalNonAssocRing.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (Polynomial.module.{u2, u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (Semiring.toModule.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.id.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (Lagrange.interpolate.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r) (Finset.sum.{u2, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (NonAssocRing.toNonUnitalNonAssocRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Ring.toNonAssocRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (CommRing.toRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (EuclideanDomain.toCommRing.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1))))))) s (fun (i : ι) => HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) r) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (Polynomial.mul'.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Lagrange.nodalWeight.{u2, u1} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i)) (HDiv.hDiv.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHDiv.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.instDivPolynomialToSemiringToDivisionSemiringToSemifield.{u2} F _inst_1)) (Lagrange.nodal.{u2, u1} F _inst_1 ι s v) (HSub.hSub.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (v i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHSub.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.sub.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (Polynomial.X.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F 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(Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (r i))))
+Case conversion may be inaccurate. Consider using '#align lagrange.interpolate_eq_nodal_weight_mul_nodal_div_X_sub_C Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_Cₓ'. -/
+theorem interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C :
     interpolate s v r = ∑ i in s, C (nodalWeight s v i) * (nodal s v / (X - C (v i))) * C (r i) :=
   sum_congr rfl fun j hj => by rw [mul_comm, basis_eq_prod_sub_inv_mul_nodal_div hj]
-#align lagrange.interpolate_eq_nodal_weight_mul_nodal_div_X_sub_C Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_x_sub_c
-
+#align lagrange.interpolate_eq_nodal_weight_mul_nodal_div_X_sub_C Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C
+
+/- warning: lagrange.eval_interpolate_not_at_node -> Lagrange.eval_interpolate_not_at_node is a dubious translation:
+lean 3 declaration is
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(AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))) x (v i)))) (r i)))))
+but is expected to have type
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} (r : ι -> F) {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (LinearMap.{u1, u1, max u1 u2, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (ι -> F) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F 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_inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) 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F _inst_1)))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))) (r i)))))
+Case conversion may be inaccurate. Consider using '#align lagrange.eval_interpolate_not_at_node Lagrange.eval_interpolate_not_at_nodeₓ'. -/
 /-- This is the first barycentric form of the Lagrange interpolant. -/
 theorem eval_interpolate_not_at_node (hx : ∀ i ∈ s, x ≠ v i) :
     eval x (interpolate s v r) =
@@ -623,6 +925,12 @@ theorem eval_interpolate_not_at_node (hx : ∀ i ∈ s, x ≠ v i) :
   rw [← mul_assoc, mul_comm, eval_basis_not_at_node hi (hx _ hi)]
 #align lagrange.eval_interpolate_not_at_node Lagrange.eval_interpolate_not_at_node
 
+/- warning: lagrange.sum_nodal_weight_mul_inv_sub_ne_zero -> Lagrange.sum_nodalWeight_mul_inv_sub_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (Set.InjOn.{u2, u1} ι F v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s)) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Finset.Nonempty.{u2} ι s) -> (Ne.{succ u1} F (Finset.sum.{u1, u2} F ι (AddCommGroup.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toAddCommGroup.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (Distrib.toHasMul.{u1} F (Ring.toDistrib.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (DivInvMonoid.toHasInv.{u1} F (DivisionRing.toDivInvMonoid.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toHasSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (AddGroupWithOne.toAddGroup.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))) x (v i))))) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))))))
+but is expected to have type
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {s : Finset.{u2} ι} {v : ι -> F} {x : F} [_inst_2 : DecidableEq.{succ u2} ι], (Set.InjOn.{u2, u1} ι F v (Finset.toSet.{u2} ι s)) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Ne.{succ u1} F x (v i))) -> (Finset.Nonempty.{u2} ι s) -> (Ne.{succ u1} F (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i))))) (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (CommMonoidWithZero.toZero.{u1} F (CommGroupWithZero.toCommMonoidWithZero.{u1} F (Semifield.toCommGroupWithZero.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align lagrange.sum_nodal_weight_mul_inv_sub_ne_zero Lagrange.sum_nodalWeight_mul_inv_sub_ne_zeroₓ'. -/
 theorem sum_nodalWeight_mul_inv_sub_ne_zero (hvs : Set.InjOn v s) (hx : ∀ i ∈ s, x ≠ v i)
     (hs : s.Nonempty) : (∑ i in s, nodalWeight s v i * (x - v i)⁻¹) ≠ 0 :=
   @right_ne_zero_of_mul_eq_one _ _ _ (eval x (nodal s v)) _ <| by
@@ -630,6 +938,12 @@ theorem sum_nodalWeight_mul_inv_sub_ne_zero (hvs : Set.InjOn v s) (hx : ∀ i 
       (eval_interpolate_not_at_node 1 hx).symm
 #align lagrange.sum_nodal_weight_mul_inv_sub_ne_zero Lagrange.sum_nodalWeight_mul_inv_sub_ne_zero
 
+/- warning: lagrange.eval_interpolate_not_at_node' -> Lagrange.eval_interpolate_not_at_node' is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Lagrange._hyg.2583 : ι) => F) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.interpolate.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v) r)) (HDiv.hDiv.{u1, u1, u1} F F F (instHDiv.{u1} F (Field.toDiv.{u1} F _inst_1)) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))) (r i))) (Finset.sum.{u1, u2} F ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} F F F (instHMul.{u1} F (NonUnitalNonAssocRing.toMul.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Lagrange.nodalWeight.{u1, u2} F _inst_1 ι (fun (a : ι) (b : ι) => _inst_2 a b) s v i) (Inv.inv.{u1} F (Field.toInv.{u1} F _inst_1) (HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (Ring.toSub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x (v i)))))))
+Case conversion may be inaccurate. Consider using '#align lagrange.eval_interpolate_not_at_node' Lagrange.eval_interpolate_not_at_node'ₓ'. -/
 /-- This is the second barycentric form of the Lagrange interpolant. -/
 theorem eval_interpolate_not_at_node' (hvs : Set.InjOn v s) (hs : s.Nonempty)
     (hx : ∀ i ∈ s, x ≠ v i) :

70fd9563

bump to nightly-2023-04-03-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/d95bef0d215ea58c0fd7bbc4b151bf3fe952c095

8477bcac

Diff

@@ -410,14 +410,14 @@ theorem eq_interpolate_iff {f : F[X]} (hvs : Set.InjOn v s) :
 
 /-- Lagrange interpolation induces isomorphism between functions from `s`
 and polynomials of degree less than `fintype.card ι`.-/
-def funEquivDegreeLt (hvs : Set.InjOn v s) : degreeLt F s.card ≃ₗ[F] s → F
+def funEquivDegreeLt (hvs : Set.InjOn v s) : degreeLT F s.card ≃ₗ[F] s → F
     where
   toFun f i := f.1.eval (v i)
   map_add' f g := funext fun v => eval_add
   map_smul' c f := funext <| by simp
   invFun r :=
     ⟨interpolate s v fun x => if hx : x ∈ s then r ⟨x, hx⟩ else 0,
-      mem_degreeLt.2 <| degree_interpolate_lt _ hvs⟩
+      mem_degreeLT.2 <| degree_interpolate_lt _ hvs⟩
   left_inv := by
     rintro ⟨f, hf⟩
     simp only [Subtype.mk_eq_mk, Subtype.coe_mk, dite_eq_ite]

70fd9563

bump to nightly-2023-03-17-00

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

c85864d4

Diff

@@ -446,8 +446,7 @@ theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs :
         Nat.succ_add_sub_one, zero_add]
     rw [degree_basis (Set.InjOn.mono hst hvt) hi, H, WithBot.coe_add,
       WithBot.add_lt_add_iff_right (@WithBot.coe_ne_bot _ (s.card - 1))]
-    convert
-      degree_interpolate_lt _
+    convert degree_interpolate_lt _
         (hvt.mono (coe_subset.mpr (insert_subset.mpr ⟨hst hi, sdiff_subset _ _⟩)))
     rw [card_insert_of_not_mem (not_mem_sdiff_of_mem_right hi), card_sdiff hst, add_comm]
   · simp_rw [eval_finset_sum, eval_mul]

70fd9563

bump to nightly-2023-03-11-16

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

cd44fb92

Diff

@@ -138,7 +138,7 @@ def basisDivisor (x y : F) : F[X] :=
 #align lagrange.basis_divisor Lagrange.basisDivisor
 
 theorem basisDivisor_self : basisDivisor x x = 0 := by
-  simp only [basis_divisor, sub_self, inv_zero, map_zero, zero_mul]
+  simp only [basis_divisor, sub_self, inv_zero, map_zero, MulZeroClass.zero_mul]
 #align lagrange.basis_divisor_self Lagrange.basisDivisor_self
 
 theorem basisDivisor_inj (hxy : basisDivisor x y = 0) : x = y :=
@@ -178,7 +178,7 @@ theorem natDegree_basisDivisor_of_ne (hxy : x ≠ y) : (basisDivisor x y).natDeg
 
 @[simp]
 theorem eval_basisDivisor_right : eval y (basisDivisor x y) = 0 := by
-  simp only [basis_divisor, eval_mul, eval_C, eval_sub, eval_X, sub_self, mul_zero]
+  simp only [basis_divisor, eval_mul, eval_C, eval_sub, eval_X, sub_self, MulZeroClass.mul_zero]
 #align lagrange.eval_basis_divisor_right Lagrange.eval_basisDivisor_right
 
 theorem eval_basisDivisor_left_of_ne (hxy : x ≠ y) : eval x (basisDivisor x y) = 1 :=
@@ -337,7 +337,7 @@ theorem eval_interpolate_at_node (hvs : Set.InjOn v s) (hi : i ∈ s) :
   rw [interpolate_apply, eval_finset_sum, ← add_sum_erase _ _ hi]
   simp_rw [eval_mul, eval_C, eval_basis_self hvs hi, mul_one, add_right_eq_self]
   refine' sum_eq_zero fun j H => _
-  rw [eval_basis_of_ne (mem_erase.mp H).1 hi, mul_zero]
+  rw [eval_basis_of_ne (mem_erase.mp H).1 hi, MulZeroClass.mul_zero]
 #align lagrange.eval_interpolate_at_node Lagrange.eval_interpolate_at_node
 
 theorem degree_interpolate_le (hvs : Set.InjOn v s) : (interpolate s v r).degree ≤ ↑(s.card - 1) :=
@@ -459,7 +459,7 @@ theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs :
         mul_one, add_right_eq_self]
       refine' sum_eq_zero fun j hj => _
       rcases mem_erase.mp hj with ⟨hij, hj⟩
-      rw [eval_basis_of_ne hij hi', mul_zero]
+      rw [eval_basis_of_ne hij hi', MulZeroClass.mul_zero]
     · have H : (∑ j in s, eval (v i) (Lagrange.basis s v j)) = 1 := by
         rw [← eval_finset_sum, sum_basis (hvt.mono hst) hs, eval_one]
       rw [← mul_one (r i), ← H, mul_sum]

70fd9563

bump to nightly-2023-03-08-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5

422cc012

Diff

@@ -134,7 +134,7 @@ variable {x y : F}
 when evaluated at `x` it gives `1` and `y` it gives `0` (where when `x = y` it is identically `0`).
 Such polynomials are the building blocks for the Lagrange interpolants. -/
 def basisDivisor (x y : F) : F[X] :=
-  c (x - y)⁻¹ * (x - c y)
+  C (x - y)⁻¹ * (X - C y)
 #align lagrange.basis_divisor Lagrange.basisDivisor
 
 theorem basisDivisor_self : basisDivisor x x = 0 := by
@@ -310,7 +310,7 @@ polynomial of degree `< s.card` that takes value `r i` on `v i` for all `i` in `
 @[simps]
 def interpolate (s : Finset ι) (v : ι → F) : (ι → F) →ₗ[F] F[X]
     where
-  toFun r := ∑ i in s, c (r i) * Lagrange.basis s v i
+  toFun r := ∑ i in s, C (r i) * Lagrange.basis s v i
   map_add' f g := by simp_rw [← Finset.sum_add_distrib, ← add_mul, ← C_add, Pi.add_apply]
   map_smul' c f := by
     simp_rw [Finset.smul_sum, C_mul', smul_smul, Pi.smul_apply, RingHom.id_apply, smul_eq_mul]
@@ -321,7 +321,7 @@ theorem interpolate_empty : interpolate ∅ v r = 0 := by rw [interpolate_apply,
 #align lagrange.interpolate_empty Lagrange.interpolate_empty
 
 @[simp]
-theorem interpolate_singleton : interpolate {i} v r = c (r i) := by
+theorem interpolate_singleton : interpolate {i} v r = C (r i) := by
   rw [interpolate_apply, sum_singleton, basis_singleton, mul_one]
 #align lagrange.interpolate_singleton Lagrange.interpolate_singleton
 
@@ -501,10 +501,10 @@ with appropriate multiplicity.
 We can use `nodal` to define the barycentric forms of the evaluated interpolant.
 -/
 def nodal (s : Finset ι) (v : ι → F) : F[X] :=
-  ∏ i in s, x - c (v i)
+  ∏ i in s, X - C (v i)
 #align lagrange.nodal Lagrange.nodal
 
-theorem nodal_eq (s : Finset ι) (v : ι → F) : nodal s v = ∏ i in s, x - c (v i) :=
+theorem nodal_eq (s : Finset ι) (v : ι → F) : nodal s v = ∏ i in s, X - C (v i) :=
   rfl
 #align lagrange.nodal_eq Lagrange.nodal_eq
 
@@ -534,22 +534,22 @@ theorem eval_nodal_not_at_node (hx : ∀ i ∈ s, x ≠ v i) : eval x (nodal s v
 #align lagrange.eval_nodal_not_at_node Lagrange.eval_nodal_not_at_node
 
 theorem nodal_eq_mul_nodal_erase [DecidableEq ι] (hi : i ∈ s) :
-    nodal s v = (x - c (v i)) * nodal (s.eraseₓ i) v := by simp_rw [nodal, mul_prod_erase _ _ hi]
+    nodal s v = (X - C (v i)) * nodal (s.eraseₓ i) v := by simp_rw [nodal, mul_prod_erase _ _ hi]
 #align lagrange.nodal_eq_mul_nodal_erase Lagrange.nodal_eq_mul_nodal_erase
 
-theorem x_sub_c_dvd_nodal (v : ι → F) (hi : i ∈ s) : x - c (v i) ∣ nodal s v :=
+theorem x_sub_c_dvd_nodal (v : ι → F) (hi : i ∈ s) : X - C (v i) ∣ nodal s v :=
   ⟨_, by classical exact nodal_eq_mul_nodal_erase hi⟩
 #align lagrange.X_sub_C_dvd_nodal Lagrange.x_sub_c_dvd_nodal
 
 variable [DecidableEq ι]
 
-theorem nodal_erase_eq_nodal_div (hi : i ∈ s) : nodal (s.eraseₓ i) v = nodal s v / (x - c (v i)) :=
+theorem nodal_erase_eq_nodal_div (hi : i ∈ s) : nodal (s.eraseₓ i) v = nodal s v / (X - C (v i)) :=
   by
   rw [nodal_eq_mul_nodal_erase hi, EuclideanDomain.mul_div_cancel_left]
   exact X_sub_C_ne_zero _
 #align lagrange.nodal_erase_eq_nodal_div Lagrange.nodal_erase_eq_nodal_div
 
-theorem nodal_insert_eq_nodal (hi : i ∉ s) : nodal (insert i s) v = (x - c (v i)) * nodal s v := by
+theorem nodal_insert_eq_nodal (hi : i ∉ s) : nodal (insert i s) v = (X - C (v i)) * nodal s v := by
   simp_rw [nodal, prod_insert hi]
 #align lagrange.nodal_insert_eq_nodal Lagrange.nodal_insert_eq_nodal
 
@@ -597,7 +597,7 @@ theorem nodalWeight_ne_zero (hvs : Set.InjOn v s) (hi : i ∈ s) : nodalWeight s
 #align lagrange.nodal_weight_ne_zero Lagrange.nodalWeight_ne_zero
 
 theorem basis_eq_prod_sub_inv_mul_nodal_div (hi : i ∈ s) :
-    Lagrange.basis s v i = c (nodalWeight s v i) * (nodal s v / (x - c (v i))) := by
+    Lagrange.basis s v i = C (nodalWeight s v i) * (nodal s v / (X - C (v i))) := by
   simp_rw [Lagrange.basis, basis_divisor, nodal_weight, prod_mul_distrib, map_prod, ←
     nodal_erase_eq_nodal_div hi, nodal]
 #align lagrange.basis_eq_prod_sub_inv_mul_nodal_div Lagrange.basis_eq_prod_sub_inv_mul_nodal_div
@@ -610,7 +610,7 @@ theorem eval_basis_not_at_node (hi : i ∈ s) (hxi : x ≠ v i) :
 #align lagrange.eval_basis_not_at_node Lagrange.eval_basis_not_at_node
 
 theorem interpolate_eq_nodalWeight_mul_nodal_div_x_sub_c :
-    interpolate s v r = ∑ i in s, c (nodalWeight s v i) * (nodal s v / (x - c (v i))) * c (r i) :=
+    interpolate s v r = ∑ i in s, C (nodalWeight s v i) * (nodal s v / (X - C (v i))) * C (r i) :=
   sum_congr rfl fun j hj => by rw [mul_comm, basis_eq_prod_sub_inv_mul_nodal_div hj]
 #align lagrange.interpolate_eq_nodal_weight_mul_nodal_div_X_sub_C Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_x_sub_c

70fd9563

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

70fd9563

feat: Axiomatise b ≠ 0 → a * b / b = a (#12424)

This lets us unify a few lemmas between GroupWithZero and EuclideanDomain and two lemmas that were previously proved separately for Nat, Int, Polynomial.

ea608559

Diff

@@ -627,7 +627,7 @@ theorem nodalWeight_eq_eval_nodal_erase_inv :
 
 theorem nodal_erase_eq_nodal_div (hi : i ∈ s) :
     nodal (s.erase i) v = nodal s v / (X - C (v i)) := by
-  rw [nodal_eq_mul_nodal_erase hi, EuclideanDomain.mul_div_cancel_left]
+  rw [nodal_eq_mul_nodal_erase hi, mul_div_cancel_left₀]
   exact X_sub_C_ne_zero _
 #align lagrange.nodal_erase_eq_nodal_div Lagrange.nodal_erase_eq_nodal_div

70fd9563

chore: superfluous parentheses (#12116)

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

596d5eca

Diff

@@ -534,7 +534,7 @@ rcases s.eq_empty_or_nonempty with (rfl | h)
 
 @[simp]
 theorem degree_nodal [Nontrivial R] : (nodal s v).degree = s.card := by
-  simp_rw [degree_eq_natDegree (nodal_ne_zero), natDegree_nodal]
+  simp_rw [degree_eq_natDegree nodal_ne_zero, natDegree_nodal]
 #align lagrange.degree_nodal Lagrange.degree_nodal
 
 theorem nodal_monic : (nodal s v).Monic :=

70fd9563

style: replace '.-/' by '. -/' (#11938)

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

3556ded2

Diff

@@ -418,7 +418,7 @@ theorem eq_interpolate_iff {f : F[X]} (hvs : Set.InjOn v s) :
 #align lagrange.eq_interpolate_iff Lagrange.eq_interpolate_iff
 
 /-- Lagrange interpolation induces isomorphism between functions from `s`
-and polynomials of degree less than `Fintype.card ι`.-/
+and polynomials of degree less than `Fintype.card ι`. -/
 def funEquivDegreeLT (hvs : Set.InjOn v s) : degreeLT F s.card ≃ₗ[F] s → F where
   toFun f i := f.1.eval (v i)
   map_add' f g := funext fun v => eval_add

70fd9563

chore: avoid Ne.def (adaptation for nightly-2024-03-27) (#11801)

1b40c7bc

Diff

@@ -166,7 +166,7 @@ theorem basisDivisor_eq_zero_iff : basisDivisor x y = 0 ↔ x = y :=
 #align lagrange.basis_divisor_eq_zero_iff Lagrange.basisDivisor_eq_zero_iff
 
 theorem basisDivisor_ne_zero_iff : basisDivisor x y ≠ 0 ↔ x ≠ y := by
-  rw [Ne.def, basisDivisor_eq_zero_iff]
+  rw [Ne, basisDivisor_eq_zero_iff]
 #align lagrange.basis_divisor_ne_zero_iff Lagrange.basisDivisor_ne_zero_iff
 
 theorem degree_basisDivisor_of_ne (hxy : x ≠ y) : (basisDivisor x y).degree = 1 := by
@@ -236,7 +236,7 @@ theorem basis_pair_right (hij : i ≠ j) : Lagrange.basis {i, j} v j = basisDivi
 #align lagrange.basis_pair_right Lagrange.basis_pair_right
 
 theorem basis_ne_zero (hvs : Set.InjOn v s) (hi : i ∈ s) : Lagrange.basis s v i ≠ 0 := by
-  simp_rw [Lagrange.basis, prod_ne_zero_iff, Ne.def, mem_erase]
+  simp_rw [Lagrange.basis, prod_ne_zero_iff, Ne, mem_erase]
   rintro j ⟨hij, hj⟩
   rw [basisDivisor_eq_zero_iff, hvs.eq_iff hi hj]
   exact hij.symm
@@ -262,12 +262,12 @@ theorem eval_basis_of_ne (hij : i ≠ j) (hj : j ∈ s) : (Lagrange.basis s v i)
 theorem natDegree_basis (hvs : Set.InjOn v s) (hi : i ∈ s) :
     (Lagrange.basis s v i).natDegree = s.card - 1 := by
   have H : ∀ j, j ∈ s.erase i → basisDivisor (v i) (v j) ≠ 0 := by
-    simp_rw [Ne.def, mem_erase, basisDivisor_eq_zero_iff]
+    simp_rw [Ne, mem_erase, basisDivisor_eq_zero_iff]
     exact fun j ⟨hij₁, hj⟩ hij₂ => hij₁ (hvs hj hi hij₂.symm)
   rw [← card_erase_of_mem hi, card_eq_sum_ones]
   convert natDegree_prod _ _ H using 1
   refine' sum_congr rfl fun j hj => (natDegree_basisDivisor_of_ne _).symm
-  rw [Ne.def, ← basisDivisor_eq_zero_iff]
+  rw [Ne, ← basisDivisor_eq_zero_iff]
   exact H _ hj
 #align lagrange.nat_degree_basis Lagrange.natDegree_basis

70fd9563

chore: classify simp can prove porting notes (#11120)

Classifies by adding issue number #10618 to porting notes claiming anything semantically equivalent to

"simp can prove this"
"simp can simplify this`"
"was @[simp], now can be proved by simp"
"was @[simp], but simp can prove it"
"removed simp attribute as the equality can already be obtained by simp"
"simp can already prove this"
"simp already proves this"
"simp can prove these"

2b4e5531

Diff

@@ -327,12 +327,12 @@ def interpolate (s : Finset ι) (v : ι → F) : (ι → F) →ₗ[F] F[X] where
     simp_rw [Finset.smul_sum, C_mul', smul_smul, Pi.smul_apply, RingHom.id_apply, smul_eq_mul]
 #align lagrange.interpolate Lagrange.interpolate
 
--- Porting note: There was originally '@[simp]' on this line but it was removed because
+-- Porting note (#10618): There was originally '@[simp]' on this line but it was removed because
 -- 'simp' could prove 'interpolate_empty'
 theorem interpolate_empty : interpolate ∅ v r = 0 := by rw [interpolate_apply, sum_empty]
 #align lagrange.interpolate_empty Lagrange.interpolate_empty
 
--- Porting note: There was originally '@[simp]' on this line but it was removed because
+-- Porting note (#10618): There was originally '@[simp]' on this line but it was removed because
 -- 'simp' could prove 'interpolate_singleton'
 theorem interpolate_singleton : interpolate {i} v r = C (r i) := by
   rw [interpolate_apply, sum_singleton, basis_singleton, mul_one]

70fd9563

chore: remove terminal, terminal refines (#10762)

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

ea36aa7d

Diff

@@ -640,7 +640,7 @@ theorem nodalWeight_ne_zero (hvs : Set.InjOn v s) (hi : i ∈ s) : nodalWeight s
   rw [nodalWeight, prod_ne_zero_iff]
   intro j hj
   rcases mem_erase.mp hj with ⟨hij, hj⟩
-  refine' inv_ne_zero (sub_ne_zero_of_ne (mt (hvs.eq_iff hi hj).mp hij.symm))
+  exact inv_ne_zero (sub_ne_zero_of_ne (mt (hvs.eq_iff hi hj).mp hij.symm))
 #align lagrange.nodal_weight_ne_zero Lagrange.nodalWeight_ne_zero
 
 end NodalWeight

70fd9563

chore: Improve Finset lemma names (#8894)

Change a few lemma names that have historically bothered me.

Finset.card_le_of_subset → Finset.card_le_card
Multiset.card_le_of_le → Multiset.card_le_card
Multiset.card_lt_of_lt → Multiset.card_lt_card
Set.ncard_le_of_subset → Set.ncard_le_ncard
Finset.image_filter → Finset.filter_image
CompleteLattice.finset_sup_compact_of_compact → CompleteLattice.isCompactElement_finset_sup

7d3d6e43

Diff

@@ -448,7 +448,7 @@ theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs :
   · simp_rw [Nat.cast_withBot, Finset.sup_lt_iff (WithBot.bot_lt_coe t.card), degree_mul]
     intro i hi
     have hs : 1 ≤ s.card := Nonempty.card_pos ⟨_, hi⟩
-    have hst' : s.card ≤ t.card := card_le_of_subset hst
+    have hst' : s.card ≤ t.card := card_le_card hst
     have H : t.card = 1 + (t.card - s.card) + (s.card - 1) := by
       rw [add_assoc, tsub_add_tsub_cancel hst' hs, ← add_tsub_assoc_of_le (hs.trans hst'),
         Nat.succ_add_sub_one, zero_add]

70fd9563

chore: exactly 4 spaces in theorems (#7328)

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

d3263b23

Diff

@@ -551,7 +551,7 @@ theorem eval_nodal_at_node {i : ι} (hi : i ∈ s) : eval (v i) (nodal s v) = 0
 #align lagrange.eval_nodal_at_node Lagrange.eval_nodal_at_node
 
 theorem eval_nodal_not_at_node [Nontrivial R] [NoZeroDivisors R] {x : R}
-(hx : ∀ i ∈ s, x ≠ v i) : eval x (nodal s v) ≠ 0 := by
+    (hx : ∀ i ∈ s, x ≠ v i) : eval x (nodal s v) ≠ 0 := by
   simp_rw [nodal, eval_prod, prod_ne_zero_iff, eval_sub, eval_X, eval_C, sub_ne_zero]
   exact hx
 #align lagrange.eval_nodal_not_at_node Lagrange.eval_nodal_not_at_node

70fd9563

chore: only four spaces for subsequent lines (#7286)

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

0c7d6fa5

Diff

@@ -567,12 +567,12 @@ set_option linter.uppercaseLean3 false in
 #align lagrange.X_sub_C_dvd_nodal Lagrange.X_sub_C_dvd_nodal
 
 theorem nodal_insert_eq_nodal [DecidableEq ι] {i : ι} (hi : i ∉ s) :
-nodal (insert i s) v = (X - C (v i)) * nodal s v := by
+    nodal (insert i s) v = (X - C (v i)) * nodal s v := by
   simp_rw [nodal, prod_insert hi]
 #align lagrange.nodal_insert_eq_nodal Lagrange.nodal_insert_eq_nodal
 
 theorem derivative_nodal [DecidableEq ι] :
-derivative (nodal s v) = ∑ i in s, nodal (s.erase i) v := by
+    derivative (nodal s v) = ∑ i in s, nodal (s.erase i) v := by
   refine' s.induction_on _ fun i t hit IH => _
   · rw [nodal_empty, derivative_one, sum_empty]
   · rw [nodal_insert_eq_nodal hit, derivative_mul, IH, derivative_sub, derivative_X, derivative_C,

70fd9563

feat(LinearAlgebra/Lagrange): Generalize typeclasses. (#6714)

Generalize some key definitions in the definition of Lagrange interpolation.

In particular, the definition of the nodal polynomial does not need to be over a field.

bf8d6d9e

Diff

@@ -139,10 +139,8 @@ namespace Lagrange
 
 open Polynomial
 
-variable {F : Type*} [Field F]
-
 section BasisDivisor
-
+variable {F : Type*} [Field F]
 variable {x y : F}
 
 /-- `basisDivisor x y` is the unique linear or constant polynomial such that
@@ -203,9 +201,10 @@ end BasisDivisor
 
 section Basis
 
-open Finset
+variable {F : Type*} [Field F] {ι : Type*} [DecidableEq ι]
+variable {s : Finset ι} {v : ι → F} {i j : ι}
 
-variable {ι : Type*} [DecidableEq ι] {s : Finset ι} {v : ι → F} {i j : ι}
+open Finset
 
 /-- Lagrange basis polynomials indexed by `s : Finset ι`, defined at nodes `v i` for a
 map `v : ι → F`. For `i, j ∈ s`, `basis s v i` evaluates to 0 at `v j` for `i ≠ j`. When
@@ -307,9 +306,10 @@ end Basis
 
 section Interpolate
 
-open Finset
+variable {F : Type*} [Field F] {ι : Type*} [DecidableEq ι]
+variable {s t : Finset ι} {i j : ι} {v : ι → F} (r r' : ι → F)
 
-variable {ι : Type*} [DecidableEq ι] {s t : Finset ι} {i j : ι} {v : ι → F} (r r' : ι → F)
+open Finset
 
 /-- Lagrange interpolation: given a finset `s : Finset ι`, a nodal map `v : ι → F` injective on
 `s` and a value function `r : ι → F`, `interpolate s v r` is the unique
@@ -495,9 +495,10 @@ end Interpolate
 
 section Nodal
 
-open Finset Polynomial
+variable {R : Type*} [CommRing R] {ι : Type*}
+variable {s : Finset ι} {v : ι → R}
 
-variable {ι : Type*} {s : Finset ι} {v : ι → F} {i : ι} (r : ι → F) {x : F}
+open Finset Polynomial
 
 /-- `nodal s v` is the unique monic polynomial whose roots are the nodes defined by `v` and `s`.
 
@@ -507,11 +508,11 @@ with appropriate multiplicity.
 We can use `nodal` to define the barycentric forms of the evaluated interpolant.
 -/
 
-def nodal (s : Finset ι) (v : ι → F) : F[X] :=
+def nodal (s : Finset ι) (v : ι → R) : R[X] :=
   ∏ i in s, (X - C (v i))
 #align lagrange.nodal Lagrange.nodal
 
-theorem nodal_eq (s : Finset ι) (v : ι → F) : nodal s v = ∏ i in s, (X - C (v i)) :=
+theorem nodal_eq (s : Finset ι) (v : ι → R) : nodal s v = ∏ i in s, (X - C (v i)) :=
   rfl
 #align lagrange.nodal_eq Lagrange.nodal_eq
 
@@ -521,67 +522,99 @@ theorem nodal_empty : nodal ∅ v = 1 := by
 #align lagrange.nodal_empty Lagrange.nodal_empty
 
 @[simp]
-theorem degree_nodal : (nodal s v).degree = s.card := by
-  simp_rw [nodal, degree_prod, degree_X_sub_C, sum_const, Nat.smul_one_eq_coe]
+theorem natDegree_nodal [Nontrivial R] : (nodal s v).natDegree = s.card := by
+  simp_rw [nodal, natDegree_prod_of_monic (h := fun i _ => monic_X_sub_C (v i)),
+    natDegree_X_sub_C, sum_const, smul_eq_mul, mul_one]
+
+theorem nodal_ne_zero [Nontrivial R] : nodal s v ≠ 0 := by
+rcases s.eq_empty_or_nonempty with (rfl | h)
+· exact one_ne_zero
+· apply ne_zero_of_natDegree_gt (n := 0)
+  simp only [natDegree_nodal, h.card_pos]
+
+@[simp]
+theorem degree_nodal [Nontrivial R] : (nodal s v).degree = s.card := by
+  simp_rw [degree_eq_natDegree (nodal_ne_zero), natDegree_nodal]
 #align lagrange.degree_nodal Lagrange.degree_nodal
 
 theorem nodal_monic : (nodal s v).Monic :=
   monic_prod_of_monic s (fun i ↦ X - C (v i)) fun i _ ↦ monic_X_sub_C (v i)
 
-theorem eval_nodal {x : F} : (nodal s v).eval x = ∏ i in s, (x - v i) := by
+theorem eval_nodal {x : R} : (nodal s v).eval x = ∏ i in s, (x - v i) := by
   simp_rw [nodal, eval_prod, eval_sub, eval_X, eval_C]
 #align lagrange.eval_nodal Lagrange.eval_nodal
 
-theorem eval_nodal_at_node (hi : i ∈ s) : eval (v i) (nodal s v) = 0 := by
-  rw [eval_nodal, prod_eq_zero_iff]
-  exact ⟨i, hi, sub_eq_zero_of_eq rfl⟩
+theorem eval_nodal_at_node {i : ι} (hi : i ∈ s) : eval (v i) (nodal s v) = 0 := by
+  rw [eval_nodal]
+  exact s.prod_eq_zero hi (sub_self (v i))
+
 #align lagrange.eval_nodal_at_node Lagrange.eval_nodal_at_node
 
-theorem eval_nodal_not_at_node (hx : ∀ i ∈ s, x ≠ v i) : eval x (nodal s v) ≠ 0 := by
+theorem eval_nodal_not_at_node [Nontrivial R] [NoZeroDivisors R] {x : R}
+(hx : ∀ i ∈ s, x ≠ v i) : eval x (nodal s v) ≠ 0 := by
   simp_rw [nodal, eval_prod, prod_ne_zero_iff, eval_sub, eval_X, eval_C, sub_ne_zero]
   exact hx
 #align lagrange.eval_nodal_not_at_node Lagrange.eval_nodal_not_at_node
 
-theorem nodal_eq_mul_nodal_erase [DecidableEq ι] (hi : i ∈ s) :
+theorem nodal_eq_mul_nodal_erase [DecidableEq ι] {i : ι} (hi : i ∈ s) :
     nodal s v = (X - C (v i)) * nodal (s.erase i) v := by
     simp_rw [nodal, Finset.mul_prod_erase _ (fun x => X - C (v x)) hi]
 #align lagrange.nodal_eq_mul_nodal_erase Lagrange.nodal_eq_mul_nodal_erase
 
-theorem X_sub_C_dvd_nodal (v : ι → F) (hi : i ∈ s) : X - C (v i) ∣ nodal s v :=
+theorem X_sub_C_dvd_nodal (v : ι → R) {i : ι} (hi : i ∈ s) : X - C (v i) ∣ nodal s v :=
   ⟨_, by classical exact nodal_eq_mul_nodal_erase hi⟩
 set_option linter.uppercaseLean3 false in
 #align lagrange.X_sub_C_dvd_nodal Lagrange.X_sub_C_dvd_nodal
 
-variable [DecidableEq ι]
-
-theorem nodal_erase_eq_nodal_div (hi : i ∈ s) :
-    nodal (s.erase i) v = nodal s v / (X - C (v i)) := by
-  rw [nodal_eq_mul_nodal_erase hi, EuclideanDomain.mul_div_cancel_left]
-  exact X_sub_C_ne_zero _
-#align lagrange.nodal_erase_eq_nodal_div Lagrange.nodal_erase_eq_nodal_div
-
-theorem nodal_insert_eq_nodal (hi : i ∉ s) : nodal (insert i s) v = (X - C (v i)) * nodal s v := by
+theorem nodal_insert_eq_nodal [DecidableEq ι] {i : ι} (hi : i ∉ s) :
+nodal (insert i s) v = (X - C (v i)) * nodal s v := by
   simp_rw [nodal, prod_insert hi]
 #align lagrange.nodal_insert_eq_nodal Lagrange.nodal_insert_eq_nodal
 
-theorem derivative_nodal : Polynomial.derivative (nodal s v) = ∑ i in s, nodal (s.erase i) v := by
-  refine' Finset.induction_on s _ fun _ _ hit IH => _
+theorem derivative_nodal [DecidableEq ι] :
+derivative (nodal s v) = ∑ i in s, nodal (s.erase i) v := by
+  refine' s.induction_on _ fun i t hit IH => _
   · rw [nodal_empty, derivative_one, sum_empty]
   · rw [nodal_insert_eq_nodal hit, derivative_mul, IH, derivative_sub, derivative_X, derivative_C,
       sub_zero, one_mul, sum_insert hit, mul_sum, erase_insert hit, add_right_inj]
     refine' sum_congr rfl fun j hjt => _
-    rw [nodal_erase_eq_nodal_div (mem_insert_of_mem hjt), nodal_insert_eq_nodal hit,
-      EuclideanDomain.mul_div_assoc _ (X_sub_C_dvd_nodal v hjt), nodal_erase_eq_nodal_div hjt]
+    rw [t.erase_insert_of_ne (ne_of_mem_of_not_mem hjt hit).symm,
+      nodal_insert_eq_nodal (mem_of_mem_erase.mt hit)]
 #align lagrange.derivative_nodal Lagrange.derivative_nodal
 
-theorem eval_nodal_derivative_eval_node_eq (hi : i ∈ s) :
-    eval (v i) (Polynomial.derivative (nodal s v)) = eval (v i) (nodal (s.erase i) v) := by
+theorem eval_nodal_derivative_eval_node_eq [DecidableEq ι] {i : ι} (hi : i ∈ s) :
+    eval (v i) (derivative (nodal s v)) = eval (v i) (nodal (s.erase i) v) := by
   rw [derivative_nodal, eval_finset_sum, ← add_sum_erase _ _ hi, add_right_eq_self]
-  refine' sum_eq_zero fun j hj => _
-  simp_rw [nodal, eval_prod, eval_sub, eval_X, eval_C, prod_eq_zero_iff, mem_erase]
-  exact ⟨i, ⟨(mem_erase.mp hj).1.symm, hi⟩, sub_eq_zero_of_eq rfl⟩
+  exact sum_eq_zero fun j hj => (eval_nodal_at_node (mem_erase.mpr ⟨(mem_erase.mp hj).1.symm, hi⟩))
 #align lagrange.eval_nodal_derivative_eval_node_eq Lagrange.eval_nodal_derivative_eval_node_eq
 
+/-- The vanishing polynomial on a multiplicative subgroup is of the form X ^ n - 1. -/
+@[simp] theorem nodal_subgroup_eq_X_pow_card_sub_one [IsDomain R]
+  (G : Subgroup Rˣ) [Fintype G] :
+  nodal (G : Set Rˣ).toFinset ((↑) : Rˣ → R) = X ^ (Fintype.card G) - 1 := by
+  have h : degree (1 : R[X]) < degree ((X : R[X]) ^ Fintype.card G) := by simp [Fintype.card_pos]
+  apply eq_of_degree_le_of_eval_index_eq (v := ((↑) : Rˣ → R)) (G : Set Rˣ).toFinset
+  · exact Set.injOn_of_injective Units.ext _
+  · simp
+  · rw [degree_sub_eq_left_of_degree_lt h, degree_nodal, Set.toFinset_card, degree_pow, degree_X,
+      nsmul_eq_mul, mul_one, Nat.cast_inj]
+    exact rfl
+  · rw [nodal_monic, leadingCoeff_sub_of_degree_lt h, monic_X_pow]
+  · intros i hi
+    rw [eval_nodal_at_node hi]
+    replace hi : i ∈ G := by simpa using hi
+    obtain ⟨g, rfl⟩ : ∃ g : G, g.val = i := ⟨⟨i, hi⟩, rfl⟩
+    simp [← Units.val_pow_eq_pow_val, ← Subgroup.coe_pow G]
+
+end Nodal
+
+section NodalWeight
+
+variable {F : Type*} [Field F] {ι : Type*} [DecidableEq ι]
+variable {s : Finset ι} {v : ι → F} {i : ι}
+
+open Finset
+
 /-- This defines the nodal weight for a given set of node indexes and node mapping function `v`. -/
 def nodalWeight (s : Finset ι) (v : ι → F) (i : ι) :=
   ∏ j in s.erase i, (v i - v j)⁻¹
@@ -592,6 +625,12 @@ theorem nodalWeight_eq_eval_nodal_erase_inv :
   rw [eval_nodal, nodalWeight, prod_inv_distrib]
 #align lagrange.nodal_weight_eq_eval_nodal_erase_inv Lagrange.nodalWeight_eq_eval_nodal_erase_inv
 
+theorem nodal_erase_eq_nodal_div (hi : i ∈ s) :
+    nodal (s.erase i) v = nodal s v / (X - C (v i)) := by
+  rw [nodal_eq_mul_nodal_erase hi, EuclideanDomain.mul_div_cancel_left]
+  exact X_sub_C_ne_zero _
+#align lagrange.nodal_erase_eq_nodal_div Lagrange.nodal_erase_eq_nodal_div
+
 theorem nodalWeight_eq_eval_nodal_derative (hi : i ∈ s) :
     nodalWeight s v i = (eval (v i) (Polynomial.derivative (nodal s v)))⁻¹ := by
   rw [eval_nodal_derivative_eval_node_eq hi, nodalWeight_eq_eval_nodal_erase_inv]
@@ -604,6 +643,15 @@ theorem nodalWeight_ne_zero (hvs : Set.InjOn v s) (hi : i ∈ s) : nodalWeight s
   refine' inv_ne_zero (sub_ne_zero_of_ne (mt (hvs.eq_iff hi hj).mp hij.symm))
 #align lagrange.nodal_weight_ne_zero Lagrange.nodalWeight_ne_zero
 
+end NodalWeight
+
+section LagrangeBarycentric
+
+variable {F : Type*} [Field F] {ι : Type*} [DecidableEq ι]
+variable {s : Finset ι} {v : ι → F} (r : ι → F) {i : ι} {x : F}
+
+open Finset
+
 theorem basis_eq_prod_sub_inv_mul_nodal_div (hi : i ∈ s) :
     Lagrange.basis s v i = C (nodalWeight s v i) * (nodal s v / (X - C (v i))) := by
   simp_rw [Lagrange.basis, basisDivisor, nodalWeight, prod_mul_distrib, map_prod, ←
@@ -650,23 +698,6 @@ theorem eval_interpolate_not_at_node' (hvs : Set.InjOn v s) (hs : s.Nonempty)
   simp only [mul_div_mul_left _ _ (eval_nodal_not_at_node hx), Pi.one_apply, mul_one]
 #align lagrange.eval_interpolate_not_at_node' Lagrange.eval_interpolate_not_at_node'
 
-/-- The vanishing polynomial on a multiplicative subgroup is of the form X ^ n - 1. -/
-@[simp] theorem nodal_subgroup_eq_X_pow_card_sub_one (G : Subgroup Fˣ) [Fintype G] :
-  nodal (G : Set Fˣ).toFinset ((↑) : Fˣ → F) = X ^ (Fintype.card G) - 1 := by
-  have h : degree (1 : F[X]) < degree ((X : F[X]) ^ Fintype.card G) := by simp [Fintype.card_pos]
-  apply eq_of_degree_le_of_eval_index_eq (v := ((↑) : Fˣ → F)) (G : Set Fˣ).toFinset
-  · exact Set.injOn_of_injective Units.ext _
-  · simp
-  · rw [degree_sub_eq_left_of_degree_lt h, degree_nodal, Set.toFinset_card, degree_pow, degree_X,
-      nsmul_eq_mul, mul_one, Nat.cast_inj]
-    exact rfl
-  · rw [nodal_monic, leadingCoeff_sub_of_degree_lt h, monic_X_pow]
-  · intros i hi
-    rw [eval_nodal_at_node hi]
-    replace hi : i ∈ G := by simpa using hi
-    obtain ⟨g, rfl⟩ : ∃ g : G, g.val = i := ⟨⟨i, hi⟩, rfl⟩
-    simp [← Units.val_pow_eq_pow_val, ← Subgroup.coe_pow G]
-
-end Nodal
+end LagrangeBarycentric
 
 end Lagrange

70fd9563

feat: add theorem about nodal on Subgroup (#6495)

A lemma about the vanishing polynomial.

Co-authored-by: Pratyush Mishra

c6e395dd

Diff

@@ -67,6 +67,21 @@ theorem eq_of_degrees_lt_of_eval_finset_eq (degree_f_lt : f.degree < s.card)
   rw [← mem_degreeLT]; exact Submodule.sub_mem _ degree_f_lt degree_g_lt
 #align polynomial.eq_of_degrees_lt_of_eval_finset_eq Polynomial.eq_of_degrees_lt_of_eval_finset_eq
 
+/--
+Two polynomials, with the same degree and leading coefficient, which have the same evaluation
+on a set of distinct values with cardinality equal to the degree, are equal.
+-/
+theorem eq_of_degree_le_of_eval_finset_eq
+    (h_deg_le : f.degree ≤ s.card)
+    (h_deg_eq : f.degree = g.degree)
+    (hlc : f.leadingCoeff = g.leadingCoeff)
+    (h_eval : ∀ x ∈ s, f.eval x = g.eval x) :
+    f = g := by
+  rcases eq_or_ne f 0 with rfl | hf
+  · rwa [degree_zero, eq_comm, degree_eq_bot, eq_comm] at h_deg_eq
+  · exact eq_of_degree_sub_lt_of_eval_finset_eq s
+      (lt_of_lt_of_le (degree_sub_lt h_deg_eq hf hlc) h_deg_le) h_eval
+
 end Finset
 
 section Indexed
@@ -101,6 +116,17 @@ theorem eq_of_degrees_lt_of_eval_index_eq (hvs : Set.InjOn v s) (degree_f_lt : f
   exact Submodule.sub_mem _ degree_f_lt degree_g_lt
 #align polynomial.eq_of_degrees_lt_of_eval_index_eq Polynomial.eq_of_degrees_lt_of_eval_index_eq
 
+theorem eq_of_degree_le_of_eval_index_eq (hvs : Set.InjOn v s)
+    (h_deg_le : f.degree ≤ s.card)
+    (h_deg_eq : f.degree = g.degree)
+    (hlc : f.leadingCoeff = g.leadingCoeff)
+    (h_eval : ∀ i ∈ s, f.eval (v i) = g.eval (v i)) : f = g := by
+  rcases eq_or_ne f 0 with rfl | hf
+  · rwa [degree_zero, eq_comm, degree_eq_bot, eq_comm] at h_deg_eq
+  · exact eq_of_degree_sub_lt_of_eval_index_eq s hvs
+      (lt_of_lt_of_le (degree_sub_lt h_deg_eq hf hlc) h_deg_le)
+      h_eval
+
 end Indexed
 
 end Polynomial
@@ -494,10 +520,14 @@ theorem nodal_empty : nodal ∅ v = 1 := by
   rfl
 #align lagrange.nodal_empty Lagrange.nodal_empty
 
+@[simp]
 theorem degree_nodal : (nodal s v).degree = s.card := by
   simp_rw [nodal, degree_prod, degree_X_sub_C, sum_const, Nat.smul_one_eq_coe]
 #align lagrange.degree_nodal Lagrange.degree_nodal
 
+theorem nodal_monic : (nodal s v).Monic :=
+  monic_prod_of_monic s (fun i ↦ X - C (v i)) fun i _ ↦ monic_X_sub_C (v i)
+
 theorem eval_nodal {x : F} : (nodal s v).eval x = ∏ i in s, (x - v i) := by
   simp_rw [nodal, eval_prod, eval_sub, eval_X, eval_C]
 #align lagrange.eval_nodal Lagrange.eval_nodal
@@ -620,6 +650,23 @@ theorem eval_interpolate_not_at_node' (hvs : Set.InjOn v s) (hs : s.Nonempty)
   simp only [mul_div_mul_left _ _ (eval_nodal_not_at_node hx), Pi.one_apply, mul_one]
 #align lagrange.eval_interpolate_not_at_node' Lagrange.eval_interpolate_not_at_node'
 
+/-- The vanishing polynomial on a multiplicative subgroup is of the form X ^ n - 1. -/
+@[simp] theorem nodal_subgroup_eq_X_pow_card_sub_one (G : Subgroup Fˣ) [Fintype G] :
+  nodal (G : Set Fˣ).toFinset ((↑) : Fˣ → F) = X ^ (Fintype.card G) - 1 := by
+  have h : degree (1 : F[X]) < degree ((X : F[X]) ^ Fintype.card G) := by simp [Fintype.card_pos]
+  apply eq_of_degree_le_of_eval_index_eq (v := ((↑) : Fˣ → F)) (G : Set Fˣ).toFinset
+  · exact Set.injOn_of_injective Units.ext _
+  · simp
+  · rw [degree_sub_eq_left_of_degree_lt h, degree_nodal, Set.toFinset_card, degree_pow, degree_X,
+      nsmul_eq_mul, mul_one, Nat.cast_inj]
+    exact rfl
+  · rw [nodal_monic, leadingCoeff_sub_of_degree_lt h, monic_X_pow]
+  · intros i hi
+    rw [eval_nodal_at_node hi]
+    replace hi : i ∈ G := by simpa using hi
+    obtain ⟨g, rfl⟩ : ∃ g : G, g.val = i := ⟨⟨i, hi⟩, rfl⟩
+    simp [← Units.val_pow_eq_pow_val, ← Subgroup.coe_pow G]
+
 end Nodal
 
 end Lagrange

70fd9563

chore: drop MulZeroClass. in mul_zero/zero_mul (#6682)

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

277dea95

Diff

@@ -127,7 +127,7 @@ def basisDivisor (x y : F) : F[X] :=
 #align lagrange.basis_divisor Lagrange.basisDivisor
 
 theorem basisDivisor_self : basisDivisor x x = 0 := by
-  simp only [basisDivisor, sub_self, inv_zero, map_zero, MulZeroClass.zero_mul]
+  simp only [basisDivisor, sub_self, inv_zero, map_zero, zero_mul]
 #align lagrange.basis_divisor_self Lagrange.basisDivisor_self
 
 theorem basisDivisor_inj (hxy : basisDivisor x y = 0) : x = y := by
@@ -165,7 +165,7 @@ theorem natDegree_basisDivisor_of_ne (hxy : x ≠ y) : (basisDivisor x y).natDeg
 
 @[simp]
 theorem eval_basisDivisor_right : eval y (basisDivisor x y) = 0 := by
-  simp only [basisDivisor, eval_mul, eval_C, eval_sub, eval_X, sub_self, MulZeroClass.mul_zero]
+  simp only [basisDivisor, eval_mul, eval_C, eval_sub, eval_X, sub_self, mul_zero]
 #align lagrange.eval_basis_divisor_right Lagrange.eval_basisDivisor_right
 
 theorem eval_basisDivisor_left_of_ne (hxy : x ≠ y) : eval x (basisDivisor x y) = 1 := by
@@ -322,7 +322,7 @@ theorem eval_interpolate_at_node (hvs : Set.InjOn v s) (hi : i ∈ s) :
   rw [interpolate_apply, eval_finset_sum, ← add_sum_erase _ _ hi]
   simp_rw [eval_mul, eval_C, eval_basis_self hvs hi, mul_one, add_right_eq_self]
   refine' sum_eq_zero fun j H => _
-  rw [eval_basis_of_ne (mem_erase.mp H).1 hi, MulZeroClass.mul_zero]
+  rw [eval_basis_of_ne (mem_erase.mp H).1 hi, mul_zero]
 #align lagrange.eval_interpolate_at_node Lagrange.eval_interpolate_at_node
 
 theorem degree_interpolate_le (hvs : Set.InjOn v s) :
@@ -440,7 +440,7 @@ theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs :
         mul_one, add_right_eq_self]
       refine' sum_eq_zero fun j hj => _
       rcases mem_erase.mp hj with ⟨hij, _⟩
-      rw [eval_basis_of_ne hij hi', MulZeroClass.mul_zero]
+      rw [eval_basis_of_ne hij hi', mul_zero]
     · have H : (∑ j in s, eval (v i) (Lagrange.basis s v j)) = 1 := by
         rw [← eval_finset_sum, sum_basis (hvt.mono hst) hs, eval_one]
       rw [← mul_one (r i), ← H, mul_sum]

70fd9563

chore: remove unused simps (#6632)

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

916c75c1

Diff

@@ -514,7 +514,7 @@ theorem eval_nodal_not_at_node (hx : ∀ i ∈ s, x ≠ v i) : eval x (nodal s v
 
 theorem nodal_eq_mul_nodal_erase [DecidableEq ι] (hi : i ∈ s) :
     nodal s v = (X - C (v i)) * nodal (s.erase i) v := by
-    simp_rw [nodal, mul_prod_erase _ _ hi, Finset.mul_prod_erase _ (fun x => X - C (v x)) hi]
+    simp_rw [nodal, Finset.mul_prod_erase _ (fun x => X - C (v x)) hi]
 #align lagrange.nodal_eq_mul_nodal_erase Lagrange.nodal_eq_mul_nodal_erase
 
 theorem X_sub_C_dvd_nodal (v : ι → F) (hi : i ∈ s) : X - C (v i) ∣ nodal s v :=

70fd9563

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -33,7 +33,7 @@ section PolynomialDetermination
 
 namespace Polynomial
 
-variable {R : Type _} [CommRing R] [IsDomain R] {f g : R[X]}
+variable {R : Type*} [CommRing R] [IsDomain R] {f g : R[X]}
 
 section Finset
 
@@ -73,7 +73,7 @@ section Indexed
 
 open Finset
 
-variable {ι : Type _} {v : ι → R} (s : Finset ι)
+variable {ι : Type*} {v : ι → R} (s : Finset ι)
 
 theorem eq_zero_of_degree_lt_of_eval_index_eq_zero (hvs : Set.InjOn v s)
     (degree_f_lt : f.degree < s.card) (eval_f : ∀ i ∈ s, f.eval (v i) = 0) : f = 0 := by
@@ -113,7 +113,7 @@ namespace Lagrange
 
 open Polynomial
 
-variable {F : Type _} [Field F]
+variable {F : Type*} [Field F]
 
 section BasisDivisor
 
@@ -179,7 +179,7 @@ section Basis
 
 open Finset
 
-variable {ι : Type _} [DecidableEq ι] {s : Finset ι} {v : ι → F} {i j : ι}
+variable {ι : Type*} [DecidableEq ι] {s : Finset ι} {v : ι → F} {i j : ι}
 
 /-- Lagrange basis polynomials indexed by `s : Finset ι`, defined at nodes `v i` for a
 map `v : ι → F`. For `i, j ∈ s`, `basis s v i` evaluates to 0 at `v j` for `i ≠ j`. When
@@ -283,7 +283,7 @@ section Interpolate
 
 open Finset
 
-variable {ι : Type _} [DecidableEq ι] {s t : Finset ι} {i j : ι} {v : ι → F} (r r' : ι → F)
+variable {ι : Type*} [DecidableEq ι] {s t : Finset ι} {i j : ι} {v : ι → F} (r r' : ι → F)
 
 /-- Lagrange interpolation: given a finset `s : Finset ι`, a nodal map `v : ι → F` injective on
 `s` and a value function `r : ι → F`, `interpolate s v r` is the unique
@@ -471,7 +471,7 @@ section Nodal
 
 open Finset Polynomial
 
-variable {ι : Type _} {s : Finset ι} {v : ι → F} {i : ι} (r : ι → F) {x : F}
+variable {ι : Type*} {s : Finset ι} {v : ι → F} {i : ι} (r : ι → F) {x : F}
 
 /-- `nodal s v` is the unique monic polynomial whose roots are the nodes defined by `v` and `s`.

70fd9563

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Wrenna Robson
-
-! This file was ported from Lean 3 source module linear_algebra.lagrange
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.BigOperators.Basic
 import Mathlib.LinearAlgebra.Vandermonde
 import Mathlib.RingTheory.Polynomial.Basic
 
+#align_import linear_algebra.lagrange from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"
+
 /-!
 # Lagrange interpolation

70fd9563

chore: cleanup whitespace (#5988)

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

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

12343aa5

Diff

@@ -288,8 +288,8 @@ open Finset
 
 variable {ι : Type _} [DecidableEq ι] {s t : Finset ι} {i j : ι} {v : ι → F} (r r' : ι → F)
 
-/-- Lagrange interpolation: given a finset `s : Finset ι`, a nodal map  `v : ι → F` injective on
-`s` and a value function `r : ι → F`,  `interpolate s v r` is the unique
+/-- Lagrange interpolation: given a finset `s : Finset ι`, a nodal map `v : ι → F` injective on
+`s` and a value function `r : ι → F`, `interpolate s v r` is the unique
 polynomial of degree `< s.card` that takes value `r i` on `v i` for all `i` in `s`. -/
 @[simps]
 def interpolate (s : Finset ι) (v : ι → F) : (ι → F) →ₗ[F] F[X] where

70fd9563

fix: ∑' precedence (#5615)

Also remove most superfluous parentheses around big operators (∑, ∏ and variants).
roughly the used regex: ([^a-zA-Zα-ωΑ-Ω'𝓝ℳ₀𝕂ₛ)]) $([∑∏][^()∑∏]*,[^()∑∏:]*)$ ([⊂⊆=<≤]) replaced by $1 $2 $3

03fc68aa

Diff

@@ -256,7 +256,7 @@ theorem degree_basis (hvs : Set.InjOn v s) (hi : i ∈ s) :
 
 -- Porting note: Added `Nat.cast_withBot` rewrites
 theorem sum_basis (hvs : Set.InjOn v s) (hs : s.Nonempty) :
-    (∑ j in s, Lagrange.basis s v j) = 1 := by
+    ∑ j in s, Lagrange.basis s v j = 1 := by
   refine' eq_of_degrees_lt_of_eval_index_eq s hvs (lt_of_le_of_lt (degree_sum_le _ _) _) _ _
   · rw [Nat.cast_withBot, Finset.sup_lt_iff (WithBot.bot_lt_coe s.card)]
     intro i hi

70fd9563

feat(Data.Set.Basic/Data.Finset.Basic): rename insert_subset (#5450)

Currently, (for both Set and Finset) insert_subset is an iff lemma stating that insert a s ⊆ t if and only if a ∈ t and s ⊆ t. For both types, this PR renames this lemma to insert_subset_iff, and adds an insert_subset lemma that gives the implication just in the reverse direction : namely theorem insert_subset (ha : a ∈ t) (hs : s ⊆ t) : insert a s ⊆ t .

This both aligns the naming with union_subset and union_subset_iff, and removes the need for the awkward insert_subset.mpr ⟨_,_⟩ idiom. It touches a lot of files (too many to list), but in a trivial way.

d8b62864

Diff

@@ -432,13 +432,13 @@ theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs :
     rw [degree_basis (Set.InjOn.mono hst hvt) hi, H, WithBot.coe_add, Nat.cast_withBot,
       WithBot.add_lt_add_iff_right (@WithBot.coe_ne_bot _ (s.card - 1))]
     convert degree_interpolate_lt _
-        (hvt.mono (coe_subset.mpr (insert_subset.mpr ⟨hst hi, sdiff_subset _ _⟩)))
+        (hvt.mono (coe_subset.mpr (insert_subset_iff.mpr ⟨hst hi, sdiff_subset _ _⟩)))
     rw [card_insert_of_not_mem (not_mem_sdiff_of_mem_right hi), card_sdiff hst, add_comm]
   · simp_rw [eval_finset_sum, eval_mul]
     by_cases hi' : i ∈ s
     · rw [← add_sum_erase _ _ hi', eval_basis_self (hvt.mono hst) hi',
         eval_interpolate_at_node _
-          (hvt.mono (coe_subset.mpr (insert_subset.mpr ⟨hi, sdiff_subset _ _⟩)))
+          (hvt.mono (coe_subset.mpr (insert_subset_iff.mpr ⟨hi, sdiff_subset _ _⟩)))
           (mem_insert_self _ _),
         mul_one, add_right_eq_self]
       refine' sum_eq_zero fun j hj => _
@@ -450,7 +450,7 @@ theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs :
       refine' sum_congr rfl fun j hj => _
       congr
       exact
-        eval_interpolate_at_node _ (hvt.mono (insert_subset.mpr ⟨hst hj, sdiff_subset _ _⟩))
+        eval_interpolate_at_node _ (hvt.mono (insert_subset_iff.mpr ⟨hst hj, sdiff_subset _ _⟩))
           (mem_insert.mpr (Or.inr (mem_sdiff.mpr ⟨hi, hi'⟩)))
 #align lagrange.interpolate_eq_sum_interpolate_insert_sdiff Lagrange.interpolate_eq_sum_interpolate_insert_sdiff
 
@@ -465,7 +465,7 @@ theorem interpolate_eq_add_interpolate_erase (hvs : Set.InjOn v s) (hi : i ∈ s
     sdiff_singleton_eq_erase, pair_comm,
     sdiff_insert_insert_of_mem_of_not_mem hj (not_mem_singleton.mpr hij.symm),
     sdiff_singleton_eq_erase]
-  · exact insert_subset.mpr ⟨hi, singleton_subset_iff.mpr hj⟩
+  · exact insert_subset_iff.mpr ⟨hi, singleton_subset_iff.mpr hj⟩
 #align lagrange.interpolate_eq_add_interpolate_erase Lagrange.interpolate_eq_add_interpolate_erase
 
 end Interpolate

70fd9563

chore: clean up spacing around at and goals (#5387)

Changes are of the form

some_tactic at h⊢ -> some_tactic at h ⊢
some_tactic at h -> some_tactic at h

2a870323

Diff

@@ -100,7 +100,7 @@ theorem eq_of_degree_sub_lt_of_eval_index_eq (hvs : Set.InjOn v s)
 theorem eq_of_degrees_lt_of_eval_index_eq (hvs : Set.InjOn v s) (degree_f_lt : f.degree < s.card)
     (degree_g_lt : g.degree < s.card) (eval_fg : ∀ i ∈ s, f.eval (v i) = g.eval (v i)) : f = g := by
   refine' eq_of_degree_sub_lt_of_eval_index_eq _ hvs _ eval_fg
-  rw [← mem_degreeLT] at degree_f_lt degree_g_lt⊢
+  rw [← mem_degreeLT] at degree_f_lt degree_g_lt ⊢
   exact Submodule.sub_mem _ degree_f_lt degree_g_lt
 #align polynomial.eq_of_degrees_lt_of_eval_index_eq Polynomial.eq_of_degrees_lt_of_eval_index_eq

70fd9563

chore: reenable eta, bump to nightly 2023-05-16 (#3414)

Now that leanprover/lean4#2210 has been merged, this PR:

removes all the set_option synthInstance.etaExperiment true commands (and some etaExperiment% term elaborators)
removes many but not quite all set_option maxHeartbeats commands
makes various other changes required to cope with leanprover/lean4#2210.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>

a6e1045f

Diff

@@ -288,18 +288,11 @@ open Finset
 
 variable {ι : Type _} [DecidableEq ι] {s t : Finset ι} {i j : ι} {v : ι → F} (r r' : ι → F)
 
-set_option synthInstance.etaExperiment true in
-set_option maxHeartbeats 300000 in
-set_option synthInstance.maxHeartbeats 60000 in
--- Porting note: The heartbeats were increased to find the instances needed for 'Finset.smul_sum'
--- and 'smul_smul' on line 322.
-
 /-- Lagrange interpolation: given a finset `s : Finset ι`, a nodal map  `v : ι → F` injective on
 `s` and a value function `r : ι → F`,  `interpolate s v r` is the unique
 polynomial of degree `< s.card` that takes value `r i` on `v i` for all `i` in `s`. -/
 @[simps]
-def interpolate (s : Finset ι) (v : ι → F) : @LinearMap _ _ _ _ (RingHom.id F) (ι → F) F[X] _ _ _
-  (Polynomial.module) where
+def interpolate (s : Finset ι) (v : ι → F) : (ι → F) →ₗ[F] F[X] where
   toFun r := ∑ i in s, C (r i) * Lagrange.basis s v i
   map_add' f g := by
     simp_rw [← Finset.sum_add_distrib]
@@ -310,29 +303,23 @@ def interpolate (s : Finset ι) (v : ι → F) : @LinearMap _ _ _ _ (RingHom.id
   map_smul' c f := by
     simp_rw [Finset.smul_sum, C_mul', smul_smul, Pi.smul_apply, RingHom.id_apply, smul_eq_mul]
 #align lagrange.interpolate Lagrange.interpolate
--- Porting note: The arguments for 'LinearMap' on line 301 had to be given explicitly because
--- the instance 'Module F F[X]' could not be synthetized
 
-set_option synthInstance.etaExperiment true in
 -- Porting note: There was originally '@[simp]' on this line but it was removed because
 -- 'simp' could prove 'interpolate_empty'
 theorem interpolate_empty : interpolate ∅ v r = 0 := by rw [interpolate_apply, sum_empty]
 #align lagrange.interpolate_empty Lagrange.interpolate_empty
 
-set_option synthInstance.etaExperiment true in
 -- Porting note: There was originally '@[simp]' on this line but it was removed because
 -- 'simp' could prove 'interpolate_singleton'
 theorem interpolate_singleton : interpolate {i} v r = C (r i) := by
   rw [interpolate_apply, sum_singleton, basis_singleton, mul_one]
 #align lagrange.interpolate_singleton Lagrange.interpolate_singleton
 
-set_option synthInstance.etaExperiment true in
 theorem interpolate_one (hvs : Set.InjOn v s) (hs : s.Nonempty) : interpolate s v 1 = 1 := by
   simp_rw [interpolate_apply, Pi.one_apply, map_one, one_mul]
   exact sum_basis hvs hs
 #align lagrange.interpolate_one Lagrange.interpolate_one
 
-set_option synthInstance.etaExperiment true in
 theorem eval_interpolate_at_node (hvs : Set.InjOn v s) (hi : i ∈ s) :
     eval (v i) (interpolate s v r) = r i := by
   rw [interpolate_apply, eval_finset_sum, ← add_sum_erase _ _ hi]
@@ -341,7 +328,6 @@ theorem eval_interpolate_at_node (hvs : Set.InjOn v s) (hi : i ∈ s) :
   rw [eval_basis_of_ne (mem_erase.mp H).1 hi, MulZeroClass.mul_zero]
 #align lagrange.eval_interpolate_at_node Lagrange.eval_interpolate_at_node
 
-set_option synthInstance.etaExperiment true in
 theorem degree_interpolate_le (hvs : Set.InjOn v s) :
     (interpolate s v r).degree ≤ ↑(s.card - 1) := by
   refine' (degree_sum_le _ _).trans _
@@ -353,7 +339,6 @@ theorem degree_interpolate_le (hvs : Set.InjOn v s) :
   · rw [degree_C hr, zero_add]
 #align lagrange.degree_interpolate_le Lagrange.degree_interpolate_le
 
-set_option synthInstance.etaExperiment true in
 -- Porting note: Added `Nat.cast_withBot` rewrites
 theorem degree_interpolate_lt (hvs : Set.InjOn v s) : (interpolate s v r).degree < s.card := by
   rw [Nat.cast_withBot]
@@ -365,46 +350,39 @@ theorem degree_interpolate_lt (hvs : Set.InjOn v s) : (interpolate s v r).degree
     exact Nat.sub_lt (Nonempty.card_pos h) zero_lt_one
 #align lagrange.degree_interpolate_lt Lagrange.degree_interpolate_lt
 
-set_option synthInstance.etaExperiment true in
 theorem degree_interpolate_erase_lt (hvs : Set.InjOn v s) (hi : i ∈ s) :
     (interpolate (s.erase i) v r).degree < ↑(s.card - 1) := by
   rw [← Finset.card_erase_of_mem hi]
   exact degree_interpolate_lt _ (Set.InjOn.mono (coe_subset.mpr (erase_subset _ _)) hvs)
 #align lagrange.degree_interpolate_erase_lt Lagrange.degree_interpolate_erase_lt
 
-set_option synthInstance.etaExperiment true in
 theorem values_eq_on_of_interpolate_eq (hvs : Set.InjOn v s)
     (hrr' : interpolate s v r = interpolate s v r') : ∀ i ∈ s, r i = r' i := fun _ hi => by
   rw [← eval_interpolate_at_node r hvs hi, hrr', eval_interpolate_at_node r' hvs hi]
 #align lagrange.values_eq_on_of_interpolate_eq Lagrange.values_eq_on_of_interpolate_eq
 
-set_option synthInstance.etaExperiment true in
 theorem interpolate_eq_of_values_eq_on (hrr' : ∀ i ∈ s, r i = r' i) :
     interpolate s v r = interpolate s v r' :=
   sum_congr rfl fun i hi => by rw [hrr' _ hi]
 #align lagrange.interpolate_eq_of_values_eq_on Lagrange.interpolate_eq_of_values_eq_on
 
-set_option synthInstance.etaExperiment true in
 theorem interpolate_eq_iff_values_eq_on (hvs : Set.InjOn v s) :
     interpolate s v r = interpolate s v r' ↔ ∀ i ∈ s, r i = r' i :=
   ⟨values_eq_on_of_interpolate_eq _ _ hvs, interpolate_eq_of_values_eq_on _ _⟩
 #align lagrange.interpolate_eq_iff_values_eq_on Lagrange.interpolate_eq_iff_values_eq_on
 
-set_option synthInstance.etaExperiment true in
 theorem eq_interpolate {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree < s.card) :
     f = interpolate s v fun i => f.eval (v i) :=
   eq_of_degrees_lt_of_eval_index_eq _ hvs degree_f_lt (degree_interpolate_lt _ hvs) fun _ hi =>
     (eval_interpolate_at_node (fun x ↦ eval (v x) f) hvs hi).symm
 #align lagrange.eq_interpolate Lagrange.eq_interpolate
 
-set_option synthInstance.etaExperiment true in
 theorem eq_interpolate_of_eval_eq {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree < s.card)
     (eval_f : ∀ i ∈ s, f.eval (v i) = r i) : f = interpolate s v r := by
   rw [eq_interpolate hvs degree_f_lt]
   exact interpolate_eq_of_values_eq_on _ _ eval_f
 #align lagrange.eq_interpolate_of_eval_eq Lagrange.eq_interpolate_of_eval_eq
 
-set_option synthInstance.etaExperiment true in
 /-- This is the characteristic property of the interpolation: the interpolation is the
 unique polynomial of `degree < Fintype.card ι` which takes the value of the `r i` on the `v i`.
 -/
@@ -416,7 +394,6 @@ theorem eq_interpolate_iff {f : F[X]} (hvs : Set.InjOn v s) :
     exact ⟨degree_interpolate_lt _ hvs, fun _ hi => eval_interpolate_at_node _ hvs hi⟩
 #align lagrange.eq_interpolate_iff Lagrange.eq_interpolate_iff
 
-set_option synthInstance.etaExperiment true in
 /-- Lagrange interpolation induces isomorphism between functions from `s`
 and polynomials of degree less than `Fintype.card ι`.-/
 def funEquivDegreeLT (hvs : Set.InjOn v s) : degreeLT F s.card ≃ₗ[F] s → F where
@@ -439,7 +416,6 @@ def funEquivDegreeLT (hvs : Set.InjOn v s) : degreeLT F s.card ≃ₗ[F] s → F
     exact dif_pos hi
 #align lagrange.fun_equiv_degree_lt Lagrange.funEquivDegreeLT
 
-set_option synthInstance.etaExperiment true in
 -- Porting note: Added `Nat.cast_withBot` rewrites
 theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs : s.Nonempty)
     (hst : s ⊆ t) :
@@ -478,7 +454,6 @@ theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs :
           (mem_insert.mpr (Or.inr (mem_sdiff.mpr ⟨hi, hi'⟩)))
 #align lagrange.interpolate_eq_sum_interpolate_insert_sdiff Lagrange.interpolate_eq_sum_interpolate_insert_sdiff
 
-set_option synthInstance.etaExperiment true in
 theorem interpolate_eq_add_interpolate_erase (hvs : Set.InjOn v s) (hi : i ∈ s) (hj : j ∈ s)
     (hij : i ≠ j) :
     interpolate s v r =
@@ -602,7 +577,6 @@ theorem nodalWeight_ne_zero (hvs : Set.InjOn v s) (hi : i ∈ s) : nodalWeight s
   refine' inv_ne_zero (sub_ne_zero_of_ne (mt (hvs.eq_iff hi hj).mp hij.symm))
 #align lagrange.nodal_weight_ne_zero Lagrange.nodalWeight_ne_zero
 
-set_option synthInstance.etaExperiment true in
 theorem basis_eq_prod_sub_inv_mul_nodal_div (hi : i ∈ s) :
     Lagrange.basis s v i = C (nodalWeight s v i) * (nodal s v / (X - C (v i))) := by
   simp_rw [Lagrange.basis, basisDivisor, nodalWeight, prod_mul_distrib, map_prod, ←
@@ -616,14 +590,12 @@ theorem eval_basis_not_at_node (hi : i ∈ s) (hxi : x ≠ v i) :
     mul_assoc (x - v i)⁻¹, inv_mul_cancel (sub_ne_zero_of_ne hxi), one_mul]
 #align lagrange.eval_basis_not_at_node Lagrange.eval_basis_not_at_node
 
-set_option synthInstance.etaExperiment true in
 theorem interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C :
     interpolate s v r = ∑ i in s, C (nodalWeight s v i) * (nodal s v / (X - C (v i))) * C (r i) :=
   sum_congr rfl fun j hj => by rw [mul_comm, basis_eq_prod_sub_inv_mul_nodal_div hj]
 set_option linter.uppercaseLean3 false in
 #align lagrange.interpolate_eq_nodal_weight_mul_nodal_div_X_sub_C Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C
 
-set_option synthInstance.etaExperiment true in
 /-- This is the first barycentric form of the Lagrange interpolant. -/
 theorem eval_interpolate_not_at_node (hx : ∀ i ∈ s, x ≠ v i) :
     eval x (interpolate s v r) =
@@ -640,7 +612,6 @@ theorem sum_nodalWeight_mul_inv_sub_ne_zero (hvs : Set.InjOn v s) (hx : ∀ i 
       (eval_interpolate_not_at_node 1 hx).symm
 #align lagrange.sum_nodal_weight_mul_inv_sub_ne_zero Lagrange.sum_nodalWeight_mul_inv_sub_ne_zero
 
-set_option synthInstance.etaExperiment true in
 /-- This is the second barycentric form of the Lagrange interpolant. -/
 theorem eval_interpolate_not_at_node' (hvs : Set.InjOn v s) (hs : s.Nonempty)
     (hx : ∀ i ∈ s, x ≠ v i) :

70fd9563

chore: tidy various files (#3848)

66cb7cc4

Diff

@@ -22,15 +22,11 @@ though strictly unique nodes are only defined when v is injective on s.
 * `Lagrange.basisDivisor x y`, with `x y : F`. These are the normalised irreducible factors of
 the Lagrange basis polynomials. They evaluate to `1` at `x` and `0` at `y` when `x` and `y`
 are distinct.
-* `lagrange.basis v i` with `i : ι`: the Lagrange basis polynomial that evaluates to `1` at `v i`
+* `Lagrange.basis v i` with `i : ι`: the Lagrange basis polynomial that evaluates to `1` at `v i`
 and `0` at `v j` for `i ≠ j`.
-* `lagrange.interpolate v r` where `r : ι → F` is a function from the fintype to the field: the
+* `Lagrange.interpolate v r` where `r : ι → F` is a function from the fintype to the field: the
 Lagrange interpolant that evaluates to `r i` at `x i` for all `i : ι`. The `r i` are the _values_
 associated with the _nodes_`x i`.
-* `lagrange.interpolate_at v f`, where `v : ι ↪ F` and `ι` is a fintype, and `f : F → F` is a
-function from the field to itself: this is the Lagrange interpolant that evaluates to `f (x i)`
-at `x i`, and so approximates the function `f`. This is just a special case of the general
-interpolation, where the values are given by a known function `f`.
 -/
 
 
@@ -258,20 +254,15 @@ theorem degree_basis (hvs : Set.InjOn v s) (hi : i ∈ s) :
   rw [degree_eq_natDegree (basis_ne_zero hvs hi), natDegree_basis hvs hi]
 #align lagrange.degree_basis Lagrange.degree_basis
 
--- Porting note: On lines 271 and 274, the pattern in 'WithBot.coe_lt_coe' could not be found
--- with 'rw' but it can with 'apply'
-
+-- Porting note: Added `Nat.cast_withBot` rewrites
 theorem sum_basis (hvs : Set.InjOn v s) (hs : s.Nonempty) :
     (∑ j in s, Lagrange.basis s v j) = 1 := by
   refine' eq_of_degrees_lt_of_eval_index_eq s hvs (lt_of_le_of_lt (degree_sum_le _ _) _) _ _
-  · rw [@Finset.sup_lt_iff (WithBot ℕ) ι _ _ s (fun b => degree (Lagrange.basis s v b)) ↑(card s)
-    (WithBot.bot_lt_coe s.card)]
+  · rw [Nat.cast_withBot, Finset.sup_lt_iff (WithBot.bot_lt_coe s.card)]
     intro i hi
-    rw [degree_basis hvs hi]
-    apply (@WithBot.coe_lt_coe _ (card s - 1) (card s) _).2
+    rw [degree_basis hvs hi, Nat.cast_withBot, WithBot.coe_lt_coe]
     exact Nat.pred_lt (card_ne_zero_of_mem hi)
-  · rw [degree_one, ← WithBot.coe_zero]
-    apply (@WithBot.coe_lt_coe _ 0 (card s) _).2
+  · rw [degree_one, ← WithBot.coe_zero, Nat.cast_withBot, WithBot.coe_lt_coe]
     exact Nonempty.card_pos hs
   · intro i hi
     rw [eval_finset_sum, eval_one, ← add_sum_erase _ _ hi, eval_basis_self hvs hi,
@@ -283,10 +274,10 @@ theorem sum_basis (hvs : Set.InjOn v s) (hs : s.Nonempty) :
 
 theorem basisDivisor_add_symm {x y : F} (hxy : x ≠ y) :
     basisDivisor x y + basisDivisor y x = 1 := by
-  classical rw [←
-      sum_basis (Set.injOn_of_injective Function.injective_id _) ⟨x, mem_insert_self _ {y}⟩,
-      sum_insert (not_mem_singleton.mpr hxy), sum_singleton, basis_pair_left hxy,
-      basis_pair_right hxy, id, id]
+  classical rw [
+    ← sum_basis (Set.injOn_of_injective Function.injective_id _) ⟨x, mem_insert_self _ {y}⟩,
+    sum_insert (not_mem_singleton.mpr hxy), sum_singleton, basis_pair_left hxy,
+    basis_pair_right hxy, id, id]
 #align lagrange.basis_divisor_add_symm Lagrange.basisDivisor_add_symm
 
 end Basis
@@ -319,18 +310,16 @@ def interpolate (s : Finset ι) (v : ι → F) : @LinearMap _ _ _ _ (RingHom.id
   map_smul' c f := by
     simp_rw [Finset.smul_sum, C_mul', smul_smul, Pi.smul_apply, RingHom.id_apply, smul_eq_mul]
 #align lagrange.interpolate Lagrange.interpolate
--- Porting note: The arguments for 'LinearMap' on line 310 had to be given explicitly because
+-- Porting note: The arguments for 'LinearMap' on line 301 had to be given explicitly because
 -- the instance 'Module F F[X]' could not be synthetized
 
 set_option synthInstance.etaExperiment true in
-
 -- Porting note: There was originally '@[simp]' on this line but it was removed because
 -- 'simp' could prove 'interpolate_empty'
 theorem interpolate_empty : interpolate ∅ v r = 0 := by rw [interpolate_apply, sum_empty]
 #align lagrange.interpolate_empty Lagrange.interpolate_empty
 
 set_option synthInstance.etaExperiment true in
-
 -- Porting note: There was originally '@[simp]' on this line but it was removed because
 -- 'simp' could prove 'interpolate_singleton'
 theorem interpolate_singleton : interpolate {i} v r = C (r i) := by
@@ -338,14 +327,12 @@ theorem interpolate_singleton : interpolate {i} v r = C (r i) := by
 #align lagrange.interpolate_singleton Lagrange.interpolate_singleton
 
 set_option synthInstance.etaExperiment true in
-
 theorem interpolate_one (hvs : Set.InjOn v s) (hs : s.Nonempty) : interpolate s v 1 = 1 := by
   simp_rw [interpolate_apply, Pi.one_apply, map_one, one_mul]
   exact sum_basis hvs hs
 #align lagrange.interpolate_one Lagrange.interpolate_one
 
 set_option synthInstance.etaExperiment true in
-
 theorem eval_interpolate_at_node (hvs : Set.InjOn v s) (hi : i ∈ s) :
     eval (v i) (interpolate s v r) = r i := by
   rw [interpolate_apply, eval_finset_sum, ← add_sum_erase _ _ hi]
@@ -355,7 +342,6 @@ theorem eval_interpolate_at_node (hvs : Set.InjOn v s) (hi : i ∈ s) :
 #align lagrange.eval_interpolate_at_node Lagrange.eval_interpolate_at_node
 
 set_option synthInstance.etaExperiment true in
-
 theorem degree_interpolate_le (hvs : Set.InjOn v s) :
     (interpolate s v r).degree ≤ ↑(s.card - 1) := by
   refine' (degree_sum_le _ _).trans _
@@ -368,20 +354,18 @@ theorem degree_interpolate_le (hvs : Set.InjOn v s) :
 #align lagrange.degree_interpolate_le Lagrange.degree_interpolate_le
 
 set_option synthInstance.etaExperiment true in
-
--- Porting note: On line 379, the pattern in 'WithBot.coe_lt_coe' could not be found
--- with 'rw' but it can with 'apply'
+-- Porting note: Added `Nat.cast_withBot` rewrites
 theorem degree_interpolate_lt (hvs : Set.InjOn v s) : (interpolate s v r).degree < s.card := by
+  rw [Nat.cast_withBot]
   rcases eq_empty_or_nonempty s with (rfl | h)
   · rw [interpolate_empty, degree_zero, card_empty]
     exact WithBot.bot_lt_coe _
   · refine' lt_of_le_of_lt (degree_interpolate_le _ hvs) _
-    apply (@WithBot.coe_lt_coe _ (card s - 1) (card s) _).2
+    rw [Nat.cast_withBot, WithBot.coe_lt_coe]
     exact Nat.sub_lt (Nonempty.card_pos h) zero_lt_one
 #align lagrange.degree_interpolate_lt Lagrange.degree_interpolate_lt
 
 set_option synthInstance.etaExperiment true in
-
 theorem degree_interpolate_erase_lt (hvs : Set.InjOn v s) (hi : i ∈ s) :
     (interpolate (s.erase i) v r).degree < ↑(s.card - 1) := by
   rw [← Finset.card_erase_of_mem hi]
@@ -389,28 +373,24 @@ theorem degree_interpolate_erase_lt (hvs : Set.InjOn v s) (hi : i ∈ s) :
 #align lagrange.degree_interpolate_erase_lt Lagrange.degree_interpolate_erase_lt
 
 set_option synthInstance.etaExperiment true in
-
 theorem values_eq_on_of_interpolate_eq (hvs : Set.InjOn v s)
     (hrr' : interpolate s v r = interpolate s v r') : ∀ i ∈ s, r i = r' i := fun _ hi => by
   rw [← eval_interpolate_at_node r hvs hi, hrr', eval_interpolate_at_node r' hvs hi]
 #align lagrange.values_eq_on_of_interpolate_eq Lagrange.values_eq_on_of_interpolate_eq
 
 set_option synthInstance.etaExperiment true in
-
 theorem interpolate_eq_of_values_eq_on (hrr' : ∀ i ∈ s, r i = r' i) :
     interpolate s v r = interpolate s v r' :=
   sum_congr rfl fun i hi => by rw [hrr' _ hi]
 #align lagrange.interpolate_eq_of_values_eq_on Lagrange.interpolate_eq_of_values_eq_on
 
 set_option synthInstance.etaExperiment true in
-
 theorem interpolate_eq_iff_values_eq_on (hvs : Set.InjOn v s) :
     interpolate s v r = interpolate s v r' ↔ ∀ i ∈ s, r i = r' i :=
   ⟨values_eq_on_of_interpolate_eq _ _ hvs, interpolate_eq_of_values_eq_on _ _⟩
 #align lagrange.interpolate_eq_iff_values_eq_on Lagrange.interpolate_eq_iff_values_eq_on
 
 set_option synthInstance.etaExperiment true in
-
 theorem eq_interpolate {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree < s.card) :
     f = interpolate s v fun i => f.eval (v i) :=
   eq_of_degrees_lt_of_eval_index_eq _ hvs degree_f_lt (degree_interpolate_lt _ hvs) fun _ hi =>
@@ -418,7 +398,6 @@ theorem eq_interpolate {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree
 #align lagrange.eq_interpolate Lagrange.eq_interpolate
 
 set_option synthInstance.etaExperiment true in
-
 theorem eq_interpolate_of_eval_eq {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt : f.degree < s.card)
     (eval_f : ∀ i ∈ s, f.eval (v i) = r i) : f = interpolate s v r := by
   rw [eq_interpolate hvs degree_f_lt]
@@ -426,7 +405,6 @@ theorem eq_interpolate_of_eval_eq {f : F[X]} (hvs : Set.InjOn v s) (degree_f_lt
 #align lagrange.eq_interpolate_of_eval_eq Lagrange.eq_interpolate_of_eval_eq
 
 set_option synthInstance.etaExperiment true in
-
 /-- This is the characteristic property of the interpolation: the interpolation is the
 unique polynomial of `degree < Fintype.card ι` which takes the value of the `r i` on the `v i`.
 -/
@@ -439,7 +417,6 @@ theorem eq_interpolate_iff {f : F[X]} (hvs : Set.InjOn v s) :
 #align lagrange.eq_interpolate_iff Lagrange.eq_interpolate_iff
 
 set_option synthInstance.etaExperiment true in
-
 /-- Lagrange interpolation induces isomorphism between functions from `s`
 and polynomials of degree less than `Fintype.card ι`.-/
 def funEquivDegreeLT (hvs : Set.InjOn v s) : degreeLT F s.card ≃ₗ[F] s → F where
@@ -463,28 +440,21 @@ def funEquivDegreeLT (hvs : Set.InjOn v s) : degreeLT F s.card ≃ₗ[F] s → F
 #align lagrange.fun_equiv_degree_lt Lagrange.funEquivDegreeLT
 
 set_option synthInstance.etaExperiment true in
-
--- Porting note: On lines 475 and 486, the patterns in 'Finset.sup_lt_iff' and
--- 'WithBot.add_lt_add_iff_right' could not be found with 'rw' or 'simp_rw' but they can
--- with 'apply'
+-- Porting note: Added `Nat.cast_withBot` rewrites
 theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs : s.Nonempty)
     (hst : s ⊆ t) :
     interpolate t v r = ∑ i in s, interpolate (insert i (t \ s)) v r * Lagrange.basis s v i := by
   symm
   refine' eq_interpolate_of_eval_eq _ hvt (lt_of_le_of_lt (degree_sum_le _ _) _) fun i hi => _
-  · apply (@Finset.sup_lt_iff _ _ _ _ s
-    (fun b ↦ degree ((interpolate (insert b (t \ s)) v) r * Lagrange.basis s v b)) _
-    (WithBot.bot_lt_coe t.card)).2
-    simp_rw [degree_mul]
+  · simp_rw [Nat.cast_withBot, Finset.sup_lt_iff (WithBot.bot_lt_coe t.card), degree_mul]
     intro i hi
     have hs : 1 ≤ s.card := Nonempty.card_pos ⟨_, hi⟩
     have hst' : s.card ≤ t.card := card_le_of_subset hst
     have H : t.card = 1 + (t.card - s.card) + (s.card - 1) := by
       rw [add_assoc, tsub_add_tsub_cancel hst' hs, ← add_tsub_assoc_of_le (hs.trans hst'),
         Nat.succ_add_sub_one, zero_add]
-    rw [degree_basis (Set.InjOn.mono hst hvt) hi, H, WithBot.coe_add]
-    apply (@WithBot.add_lt_add_iff_right _ _ _ (degree ((interpolate (insert i (t \ s)) v) r))
-    (↑(1 + (card t - card s))) _ _ _ (@WithBot.coe_ne_bot _ (s.card - 1))).2
+    rw [degree_basis (Set.InjOn.mono hst hvt) hi, H, WithBot.coe_add, Nat.cast_withBot,
+      WithBot.add_lt_add_iff_right (@WithBot.coe_ne_bot _ (s.card - 1))]
     convert degree_interpolate_lt _
         (hvt.mono (coe_subset.mpr (insert_subset.mpr ⟨hst hi, sdiff_subset _ _⟩)))
     rw [card_insert_of_not_mem (not_mem_sdiff_of_mem_right hi), card_sdiff hst, add_comm]
@@ -509,7 +479,6 @@ theorem interpolate_eq_sum_interpolate_insert_sdiff (hvt : Set.InjOn v t) (hs :
 #align lagrange.interpolate_eq_sum_interpolate_insert_sdiff Lagrange.interpolate_eq_sum_interpolate_insert_sdiff
 
 set_option synthInstance.etaExperiment true in
-
 theorem interpolate_eq_add_interpolate_erase (hvs : Set.InjOn v s) (hi : i ∈ s) (hj : j ∈ s)
     (hij : i ≠ j) :
     interpolate s v r =
@@ -634,7 +603,6 @@ theorem nodalWeight_ne_zero (hvs : Set.InjOn v s) (hi : i ∈ s) : nodalWeight s
 #align lagrange.nodal_weight_ne_zero Lagrange.nodalWeight_ne_zero
 
 set_option synthInstance.etaExperiment true in
-
 theorem basis_eq_prod_sub_inv_mul_nodal_div (hi : i ∈ s) :
     Lagrange.basis s v i = C (nodalWeight s v i) * (nodal s v / (X - C (v i))) := by
   simp_rw [Lagrange.basis, basisDivisor, nodalWeight, prod_mul_distrib, map_prod, ←
@@ -649,7 +617,6 @@ theorem eval_basis_not_at_node (hi : i ∈ s) (hxi : x ≠ v i) :
 #align lagrange.eval_basis_not_at_node Lagrange.eval_basis_not_at_node
 
 set_option synthInstance.etaExperiment true in
-
 theorem interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C :
     interpolate s v r = ∑ i in s, C (nodalWeight s v i) * (nodal s v / (X - C (v i))) * C (r i) :=
   sum_congr rfl fun j hj => by rw [mul_comm, basis_eq_prod_sub_inv_mul_nodal_div hj]
@@ -657,7 +624,6 @@ set_option linter.uppercaseLean3 false in
 #align lagrange.interpolate_eq_nodal_weight_mul_nodal_div_X_sub_C Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C
 
 set_option synthInstance.etaExperiment true in
-
 /-- This is the first barycentric form of the Lagrange interpolant. -/
 theorem eval_interpolate_not_at_node (hx : ∀ i ∈ s, x ≠ v i) :
     eval x (interpolate s v r) =
@@ -675,7 +641,6 @@ theorem sum_nodalWeight_mul_inv_sub_ne_zero (hvs : Set.InjOn v s) (hx : ∀ i 
 #align lagrange.sum_nodal_weight_mul_inv_sub_ne_zero Lagrange.sum_nodalWeight_mul_inv_sub_ne_zero
 
 set_option synthInstance.etaExperiment true in
-
 /-- This is the second barycentric form of the Lagrange interpolant. -/
 theorem eval_interpolate_not_at_node' (hvs : Set.InjOn v s) (hs : s.Nonempty)
     (hx : ∀ i ∈ s, x ≠ v i) :

70fd9563

chore: bye-bye, solo bys! (#3825)

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

14167e48

Diff

@@ -261,8 +261,8 @@ theorem degree_basis (hvs : Set.InjOn v s) (hi : i ∈ s) :
 -- Porting note: On lines 271 and 274, the pattern in 'WithBot.coe_lt_coe' could not be found
 -- with 'rw' but it can with 'apply'
 
-theorem sum_basis (hvs : Set.InjOn v s) (hs : s.Nonempty) : (∑ j in s, Lagrange.basis s v j) = 1 :=
-  by
+theorem sum_basis (hvs : Set.InjOn v s) (hs : s.Nonempty) :
+    (∑ j in s, Lagrange.basis s v j) = 1 := by
   refine' eq_of_degrees_lt_of_eval_index_eq s hvs (lt_of_le_of_lt (degree_sum_le _ _) _) _ _
   · rw [@Finset.sup_lt_iff (WithBot ℕ) ι _ _ s (fun b => degree (Lagrange.basis s v b)) ↑(card s)
     (WithBot.bot_lt_coe s.card)]
@@ -281,8 +281,8 @@ theorem sum_basis (hvs : Set.InjOn v s) (hs : s.Nonempty) : (∑ j in s, Lagrang
     rw [eval_basis_of_ne hij hi]
 #align lagrange.sum_basis Lagrange.sum_basis
 
-theorem basisDivisor_add_symm {x y : F} (hxy : x ≠ y) : basisDivisor x y + basisDivisor y x = 1 :=
-  by
+theorem basisDivisor_add_symm {x y : F} (hxy : x ≠ y) :
+    basisDivisor x y + basisDivisor y x = 1 := by
   classical rw [←
       sum_basis (Set.injOn_of_injective Function.injective_id _) ⟨x, mem_insert_self _ {y}⟩,
       sum_insert (not_mem_singleton.mpr hxy), sum_singleton, basis_pair_left hxy,
@@ -356,8 +356,8 @@ theorem eval_interpolate_at_node (hvs : Set.InjOn v s) (hi : i ∈ s) :
 
 set_option synthInstance.etaExperiment true in
 
-theorem degree_interpolate_le (hvs : Set.InjOn v s) : (interpolate s v r).degree ≤ ↑(s.card - 1) :=
-  by
+theorem degree_interpolate_le (hvs : Set.InjOn v s) :
+    (interpolate s v r).degree ≤ ↑(s.card - 1) := by
   refine' (degree_sum_le _ _).trans _
   rw [Finset.sup_le_iff]
   intro i hi
@@ -583,8 +583,8 @@ set_option linter.uppercaseLean3 false in
 
 variable [DecidableEq ι]
 
-theorem nodal_erase_eq_nodal_div (hi : i ∈ s) : nodal (s.erase i) v = nodal s v / (X - C (v i)) :=
-  by
+theorem nodal_erase_eq_nodal_div (hi : i ∈ s) :
+    nodal (s.erase i) v = nodal s v / (X - C (v i)) := by
   rw [nodal_eq_mul_nodal_erase hi, EuclideanDomain.mul_div_cancel_left]
   exact X_sub_C_ne_zero _
 #align lagrange.nodal_erase_eq_nodal_div Lagrange.nodal_erase_eq_nodal_div

70fd9563

feat: port LinearAlgebra.Lagrange (#3784)

7482d3ea

`linear_algebra.lagrange` ⟷ `Mathlib.LinearAlgebra.Lagrange`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 573

linear_algebra.lagrange ⟷ Mathlib.LinearAlgebra.Lagrange

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 573

`linear_algebra.lagrange` ⟷ `Mathlib.LinearAlgebra.Lagrange`