topology.continuous_function.polynomial

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

a148d797

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

bd15ff41

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -171,8 +171,8 @@ theorem polynomialFunctions.comap_compRightAlgHom_iccHomeoI (a b : ℝ) (h : a <
   ext f
   fconstructor
   · rintro ⟨p, ⟨-, w⟩⟩
-    rw [DFunLike.ext_iff] at w 
-    dsimp at w 
+    rw [DFunLike.ext_iff] at w
+    dsimp at w
     let q := p.comp ((b - a)⁻¹ • Polynomial.X + Polynomial.C (-a * (b - a)⁻¹))
     refine' ⟨q, ⟨_, _⟩⟩
     · simp

bd15ff41

bump to nightly-2024-01-19-06

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

33b57512

Diff

@@ -171,7 +171,7 @@ theorem polynomialFunctions.comap_compRightAlgHom_iccHomeoI (a b : ℝ) (h : a <
   ext f
   fconstructor
   · rintro ⟨p, ⟨-, w⟩⟩
-    rw [FunLike.ext_iff] at w 
+    rw [DFunLike.ext_iff] at w 
     dsimp at w 
     let q := p.comp ((b - a)⁻¹ • Polynomial.X + Polynomial.C (-a * (b - a)⁻¹))
     refine' ⟨q, ⟨_, _⟩⟩

bd15ff41

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) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import Mathbin.Topology.Algebra.Polynomial
-import Mathbin.Topology.ContinuousFunction.Algebra
-import Mathbin.Topology.UnitInterval
+import Topology.Algebra.Polynomial
+import Topology.ContinuousFunction.Algebra
+import Topology.UnitInterval
 
 #align_import topology.continuous_function.polynomial from "leanprover-community/mathlib"@"bd15ff41b70f5e2cc210f26f25a8d5c53b20d3de"

bd15ff41

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) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module topology.continuous_function.polynomial
-! leanprover-community/mathlib commit bd15ff41b70f5e2cc210f26f25a8d5c53b20d3de
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.Algebra.Polynomial
 import Mathbin.Topology.ContinuousFunction.Algebra
 import Mathbin.Topology.UnitInterval
 
+#align_import topology.continuous_function.polynomial from "leanprover-community/mathlib"@"bd15ff41b70f5e2cc210f26f25a8d5c53b20d3de"
+
 /-!
 # Constructions relating polynomial functions and continuous functions.

bd15ff41

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -70,6 +70,7 @@ section
 variable {α : Type _} [TopologicalSpace α] [CommSemiring R] [TopologicalSpace R]
   [TopologicalSemiring R]
 
+#print Polynomial.aeval_continuousMap_apply /-
 @[simp]
 theorem aeval_continuousMap_apply (g : R[X]) (f : C(α, R)) (x : α) :
     ((Polynomial.aeval f) g) x = g.eval (f x) :=
@@ -78,6 +79,7 @@ theorem aeval_continuousMap_apply (g : R[X]) (f : C(α, R)) (x : α) :
   · intro p q hp hq; simp [hp, hq]
   · intro n a; simp [Pi.pow_apply]
 #align polynomial.aeval_continuous_map_apply Polynomial.aeval_continuousMap_apply
+-/
 
 end
 
@@ -87,6 +89,7 @@ noncomputable section
 
 variable [CommSemiring R] [TopologicalSpace R] [TopologicalSemiring R]
 
+#print Polynomial.toContinuousMapAlgHom /-
 /-- The algebra map from `R[X]` to continuous functions `C(R, R)`.
 -/
 @[simps]
@@ -99,7 +102,9 @@ def toContinuousMapAlgHom : R[X] →ₐ[R] C(R, R)
   map_mul' := by intros; ext; simp
   commutes' := by intros; ext; simp [Algebra.algebraMap_eq_smul_one]
 #align polynomial.to_continuous_map_alg_hom Polynomial.toContinuousMapAlgHom
+-/
 
+#print Polynomial.toContinuousMapOnAlgHom /-
 /-- The algebra map from `R[X]` to continuous functions `C(X, R)`, for any subset `X` of `R`.
 -/
 @[simps]
@@ -112,6 +117,7 @@ def toContinuousMapOnAlgHom (X : Set R) : R[X] →ₐ[R] C(X, R)
   map_mul' := by intros; ext; simp
   commutes' := by intros; ext; simp [Algebra.algebraMap_eq_smul_one]
 #align polynomial.to_continuous_map_on_alg_hom Polynomial.toContinuousMapOnAlgHom
+-/
 
 end
 
@@ -121,6 +127,7 @@ section
 
 variable [CommSemiring R] [TopologicalSpace R] [TopologicalSemiring R]
 
+#print polynomialFunctions /-
 /--
 The subalgebra of polynomial functions in `C(X, R)`, for `X` a subset of some topological semiring
 `R`.
@@ -128,12 +135,15 @@ The subalgebra of polynomial functions in `C(X, R)`, for `X` a subset of some to
 def polynomialFunctions (X : Set R) : Subalgebra R C(X, R) :=
   (⊤ : Subalgebra R R[X]).map (Polynomial.toContinuousMapOnAlgHom X)
 #align polynomial_functions polynomialFunctions
+-/
 
+#print polynomialFunctions_coe /-
 @[simp]
 theorem polynomialFunctions_coe (X : Set R) :
     (polynomialFunctions X : Set C(X, R)) = Set.range (Polynomial.toContinuousMapOnAlgHom X) := by
   ext; simp [polynomialFunctions]
 #align polynomial_functions_coe polynomialFunctions_coe
+-/
 
 #print polynomialFunctions_separatesPoints /-
 -- TODO:
@@ -154,6 +164,7 @@ open scoped unitInterval
 
 open ContinuousMap
 
+#print polynomialFunctions.comap_compRightAlgHom_iccHomeoI /-
 /-- The preimage of polynomials on `[0,1]` under the pullback map by `x ↦ (b-a) * x + a`
 is the polynomials on `[a,b]`. -/
 theorem polynomialFunctions.comap_compRightAlgHom_iccHomeoI (a b : ℝ) (h : a < b) :
@@ -197,6 +208,7 @@ theorem polynomialFunctions.comap_compRightAlgHom_iccHomeoI (a b : ℝ) (h : a <
     · simp
     · ext x; simp [mul_comm]
 #align polynomial_functions.comap_comp_right_alg_hom_Icc_homeo_I polynomialFunctions.comap_compRightAlgHom_iccHomeoI
+-/
 
 end

bd15ff41

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -94,10 +94,10 @@ def toContinuousMapAlgHom : R[X] →ₐ[R] C(R, R)
     where
   toFun p := p.toContinuousMap
   map_zero' := by ext; simp
-  map_add' := by intros ; ext; simp
+  map_add' := by intros; ext; simp
   map_one' := by ext; simp
-  map_mul' := by intros ; ext; simp
-  commutes' := by intros ; ext; simp [Algebra.algebraMap_eq_smul_one]
+  map_mul' := by intros; ext; simp
+  commutes' := by intros; ext; simp [Algebra.algebraMap_eq_smul_one]
 #align polynomial.to_continuous_map_alg_hom Polynomial.toContinuousMapAlgHom
 
 /-- The algebra map from `R[X]` to continuous functions `C(X, R)`, for any subset `X` of `R`.
@@ -107,10 +107,10 @@ def toContinuousMapOnAlgHom (X : Set R) : R[X] →ₐ[R] C(X, R)
     where
   toFun p := p.toContinuousMapOn X
   map_zero' := by ext; simp
-  map_add' := by intros ; ext; simp
+  map_add' := by intros; ext; simp
   map_one' := by ext; simp
-  map_mul' := by intros ; ext; simp
-  commutes' := by intros ; ext; simp [Algebra.algebraMap_eq_smul_one]
+  map_mul' := by intros; ext; simp
+  commutes' := by intros; ext; simp [Algebra.algebraMap_eq_smul_one]
 #align polynomial.to_continuous_map_on_alg_hom Polynomial.toContinuousMapOnAlgHom
 
 end
@@ -163,8 +163,8 @@ theorem polynomialFunctions.comap_compRightAlgHom_iccHomeoI (a b : ℝ) (h : a <
   ext f
   fconstructor
   · rintro ⟨p, ⟨-, w⟩⟩
-    rw [FunLike.ext_iff] at w
-    dsimp at w
+    rw [FunLike.ext_iff] at w 
+    dsimp at w 
     let q := p.comp ((b - a)⁻¹ • Polynomial.X + Polynomial.C (-a * (b - a)⁻¹))
     refine' ⟨q, ⟨_, _⟩⟩
     · simp

bd15ff41

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -32,7 +32,7 @@ import Mathbin.Topology.UnitInterval
 
 variable {R : Type _}
 
-open Polynomial
+open scoped Polynomial
 
 namespace Polynomial
 
@@ -150,7 +150,7 @@ theorem polynomialFunctions_separatesPoints (X : Set R) : (polynomialFunctions X
 #align polynomial_functions_separates_points polynomialFunctions_separatesPoints
 -/
 
-open unitInterval
+open scoped unitInterval
 
 open ContinuousMap

bd15ff41

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -70,9 +70,6 @@ section
 variable {α : Type _} [TopologicalSpace α] [CommSemiring R] [TopologicalSpace R]
   [TopologicalSemiring R]
 
-/- warning: polynomial.aeval_continuous_map_apply -> Polynomial.aeval_continuousMap_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.aeval_continuous_map_apply Polynomial.aeval_continuousMap_applyₓ'. -/
 @[simp]
 theorem aeval_continuousMap_apply (g : R[X]) (f : C(α, R)) (x : α) :
     ((Polynomial.aeval f) g) x = g.eval (f x) :=
@@ -90,12 +87,6 @@ noncomputable section
 
 variable [CommSemiring R] [TopologicalSpace R] [TopologicalSemiring R]
 
-/- warning: polynomial.to_continuous_map_alg_hom -> Polynomial.toContinuousMapAlgHom is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSemiring.{u1} R _inst_2 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))], AlgHom.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} R R _inst_2 _inst_2) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.semiring.{u1, u1} R R _inst_2 _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) (ContinuousMap.algebra.{u1, u1, u1} R _inst_2 R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSemiring.{u1} R _inst_2 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))], AlgHom.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} R R _inst_2 _inst_2) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.instSemiringContinuousMap.{u1, u1} R R _inst_2 _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) (ContinuousMap.algebra.{u1, u1, u1} R _inst_2 R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3)
-Case conversion may be inaccurate. Consider using '#align polynomial.to_continuous_map_alg_hom Polynomial.toContinuousMapAlgHomₓ'. -/
 /-- The algebra map from `R[X]` to continuous functions `C(R, R)`.
 -/
 @[simps]
@@ -109,12 +100,6 @@ def toContinuousMapAlgHom : R[X] →ₐ[R] C(R, R)
   commutes' := by intros ; ext; simp [Algebra.algebraMap_eq_smul_one]
 #align polynomial.to_continuous_map_alg_hom Polynomial.toContinuousMapAlgHom
 
-/- warning: polynomial.to_continuous_map_on_alg_hom -> Polynomial.toContinuousMapOnAlgHom 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 polynomial.to_continuous_map_on_alg_hom Polynomial.toContinuousMapOnAlgHomₓ'. -/
 /-- The algebra map from `R[X]` to continuous functions `C(X, R)`, for any subset `X` of `R`.
 -/
 @[simps]
@@ -136,12 +121,6 @@ section
 
 variable [CommSemiring R] [TopologicalSpace R] [TopologicalSemiring R]
 
-/- warning: polynomial_functions -> polynomialFunctions is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align polynomial_functions polynomialFunctionsₓ'. -/
 /--
 The subalgebra of polynomial functions in `C(X, R)`, for `X` a subset of some topological semiring
 `R`.
@@ -150,9 +129,6 @@ def polynomialFunctions (X : Set R) : Subalgebra R C(X, R) :=
   (⊤ : Subalgebra R R[X]).map (Polynomial.toContinuousMapOnAlgHom X)
 #align polynomial_functions polynomialFunctions
 
-/- warning: polynomial_functions_coe -> polynomialFunctions_coe is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial_functions_coe polynomialFunctions_coeₓ'. -/
 @[simp]
 theorem polynomialFunctions_coe (X : Set R) :
     (polynomialFunctions X : Set C(X, R)) = Set.range (Polynomial.toContinuousMapOnAlgHom X) := by
@@ -178,9 +154,6 @@ open unitInterval
 
 open ContinuousMap
 
-/- warning: polynomial_functions.comap_comp_right_alg_hom_Icc_homeo_I -> polynomialFunctions.comap_compRightAlgHom_iccHomeoI is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial_functions.comap_comp_right_alg_hom_Icc_homeo_I polynomialFunctions.comap_compRightAlgHom_iccHomeoIₓ'. -/
 /-- The preimage of polynomials on `[0,1]` under the pullback map by `x ↦ (b-a) * x + a`
 is the polynomials on `[a,b]`. -/
 theorem polynomialFunctions.comap_compRightAlgHom_iccHomeoI (a b : ℝ) (h : a < b) :

bd15ff41

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -78,10 +78,8 @@ theorem aeval_continuousMap_apply (g : R[X]) (f : C(α, R)) (x : α) :
     ((Polynomial.aeval f) g) x = g.eval (f x) :=
   by
   apply Polynomial.induction_on' g
-  · intro p q hp hq
-    simp [hp, hq]
-  · intro n a
-    simp [Pi.pow_apply]
+  · intro p q hp hq; simp [hp, hq]
+  · intro n a; simp [Pi.pow_apply]
 #align polynomial.aeval_continuous_map_apply Polynomial.aeval_continuousMap_apply
 
 end
@@ -104,24 +102,11 @@ Case conversion may be inaccurate. Consider using '#align polynomial.to_continuo
 def toContinuousMapAlgHom : R[X] →ₐ[R] C(R, R)
     where
   toFun p := p.toContinuousMap
-  map_zero' := by
-    ext
-    simp
-  map_add' := by
-    intros
-    ext
-    simp
-  map_one' := by
-    ext
-    simp
-  map_mul' := by
-    intros
-    ext
-    simp
-  commutes' := by
-    intros
-    ext
-    simp [Algebra.algebraMap_eq_smul_one]
+  map_zero' := by ext; simp
+  map_add' := by intros ; ext; simp
+  map_one' := by ext; simp
+  map_mul' := by intros ; ext; simp
+  commutes' := by intros ; ext; simp [Algebra.algebraMap_eq_smul_one]
 #align polynomial.to_continuous_map_alg_hom Polynomial.toContinuousMapAlgHom
 
 /- warning: polynomial.to_continuous_map_on_alg_hom -> Polynomial.toContinuousMapOnAlgHom is a dubious translation:
@@ -136,24 +121,11 @@ Case conversion may be inaccurate. Consider using '#align polynomial.to_continuo
 def toContinuousMapOnAlgHom (X : Set R) : R[X] →ₐ[R] C(X, R)
     where
   toFun p := p.toContinuousMapOn X
-  map_zero' := by
-    ext
-    simp
-  map_add' := by
-    intros
-    ext
-    simp
-  map_one' := by
-    ext
-    simp
-  map_mul' := by
-    intros
-    ext
-    simp
-  commutes' := by
-    intros
-    ext
-    simp [Algebra.algebraMap_eq_smul_one]
+  map_zero' := by ext; simp
+  map_add' := by intros ; ext; simp
+  map_one' := by ext; simp
+  map_mul' := by intros ; ext; simp
+  commutes' := by intros ; ext; simp [Algebra.algebraMap_eq_smul_one]
 #align polynomial.to_continuous_map_on_alg_hom Polynomial.toContinuousMapOnAlgHom
 
 end
@@ -183,10 +155,8 @@ def polynomialFunctions (X : Set R) : Subalgebra R C(X, R) :=
 Case conversion may be inaccurate. Consider using '#align polynomial_functions_coe polynomialFunctions_coeₓ'. -/
 @[simp]
 theorem polynomialFunctions_coe (X : Set R) :
-    (polynomialFunctions X : Set C(X, R)) = Set.range (Polynomial.toContinuousMapOnAlgHom X) :=
-  by
-  ext
-  simp [polynomialFunctions]
+    (polynomialFunctions X : Set C(X, R)) = Set.range (Polynomial.toContinuousMapOnAlgHom X) := by
+  ext; simp [polynomialFunctions]
 #align polynomial_functions_coe polynomialFunctions_coe
 
 #print polynomialFunctions_separatesPoints /-
@@ -238,8 +208,7 @@ theorem polynomialFunctions.comap_compRightAlgHom_iccHomeoI (a b : ℝ) (h : a <
         simp only [iccHomeoI_symm_apply_coe, Subtype.coe_mk]
         replace h : b - a ≠ 0 := sub_ne_zero_of_ne h.ne.symm
         simp only [mul_add]
-        field_simp
-        ring
+        field_simp; ring
       · change _ + _ ∈ I
         rw [mul_comm (b - a)⁻¹, ← neg_mul, ← add_mul, ← sub_eq_add_neg]
         have w₁ : 0 < (b - a)⁻¹ := inv_pos.mpr (sub_pos.mpr h)
@@ -253,8 +222,7 @@ theorem polynomialFunctions.comap_compRightAlgHom_iccHomeoI (a b : ℝ) (h : a <
     let q := p.comp ((b - a) • Polynomial.X + Polynomial.C a)
     refine' ⟨q, ⟨_, _⟩⟩
     · simp
-    · ext x
-      simp [mul_comm]
+    · ext x; simp [mul_comm]
 #align polynomial_functions.comap_comp_right_alg_hom_Icc_homeo_I polynomialFunctions.comap_compRightAlgHom_iccHomeoI
 
 end

bd15ff41

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -71,10 +71,7 @@ variable {α : Type _} [TopologicalSpace α] [CommSemiring R] [TopologicalSpace
   [TopologicalSemiring R]
 
 /- warning: polynomial.aeval_continuous_map_apply -> Polynomial.aeval_continuousMap_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.aeval_continuous_map_apply Polynomial.aeval_continuousMap_applyₓ'. -/
 @[simp]
 theorem aeval_continuousMap_apply (g : R[X]) (f : C(α, R)) (x : α) :
@@ -182,10 +179,7 @@ def polynomialFunctions (X : Set R) : Subalgebra R C(X, R) :=
 #align polynomial_functions polynomialFunctions
 
 /- warning: polynomial_functions_coe -> polynomialFunctions_coe is a dubious translation:
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R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3)))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (AddMonoid.toAddZeroClass.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (AddCommMonoid.toAddMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3)))))) (DistribMulAction.toDistribSMul.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3))))) (Module.toDistribMulAction.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3)))) (Algebra.toModule.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3)))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3)))) (Algebra.toModule.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3)))) (Algebra.toModule.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3) (AlgHom.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3)) (AlgHom.algHomClass.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3)))))) (Polynomial.toContinuousMapOnAlgHom.{u1} R _inst_1 _inst_2 _inst_3 X)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial_functions_coe polynomialFunctions_coeₓ'. -/
 @[simp]
 theorem polynomialFunctions_coe (X : Set R) :
@@ -215,10 +209,7 @@ open unitInterval
 open ContinuousMap
 
 /- warning: polynomial_functions.comap_comp_right_alg_hom_Icc_homeo_I -> polynomialFunctions.comap_compRightAlgHom_iccHomeoI is a dubious translation:
-lean 3 declaration is
-  forall (a : Real) (b : Real) (h : LT.lt.{0} Real Real.hasLt a b), Eq.{1} (Subalgebra.{0, 0} Real (ContinuousMap.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) a b)) Real (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) a b)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) Real.commSemiring (ContinuousMap.semiring.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) a b)) Real (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) a b)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.semiring (TopologicalRing.to_topologicalSemiring.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) Real.topologicalRing)) (ContinuousMap.algebra.{0, 0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) a b)) (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) a b)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) Real Real.commSemiring Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.semiring (Algebra.id.{0} Real Real.commSemiring) (TopologicalRing.to_topologicalSemiring.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) Real.topologicalRing))) (Subalgebra.comap.{0, 0, 0} Real (ContinuousMap.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) a b)) Real (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) a b)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (ContinuousMap.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) Real.commSemiring (ContinuousMap.semiring.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) a b)) Real (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) a b)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.semiring (TopologicalRing.to_topologicalSemiring.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) Real.topologicalRing)) (ContinuousMap.algebra.{0, 0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) a b)) (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) a b)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) Real Real.commSemiring Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.semiring (Algebra.id.{0} Real Real.commSemiring) (TopologicalRing.to_topologicalSemiring.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) Real.topologicalRing)) (ContinuousMap.semiring.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (CommSemiring.toSemiring.{0} Real Real.commSemiring) (TopologicalRing.to_topologicalSemiring.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) Real.topologicalRing)) (ContinuousMap.algebra.{0, 0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) Real Real.commSemiring Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real 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(Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real (StrictOrderedRing.toRing.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} 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(NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) Real.topologicalRing) (Set.Icc.{0} Real Real.preorder a b))
-but is expected to have type
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Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) a b)) (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) a b)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) Real Real.instCommSemiringReal Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.semiring (Algebra.id.{0} Real Real.instCommSemiringReal) (TopologicalRing.toTopologicalSemiring.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) instTopologicalRingRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceToNonUnitalNonAssocRingToNonAssocRingInstRingReal)) (ContinuousMap.instSemiringContinuousMap.{0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (CommMonoidWithZero.toZero.{0} Real (CommGroupWithZero.toCommMonoidWithZero.{0} Real (Semifield.toCommGroupWithZero.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real (Semiring.toOne.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))))) Real (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (CommMonoidWithZero.toZero.{0} Real (CommGroupWithZero.toCommMonoidWithZero.{0} Real (Semifield.toCommGroupWithZero.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real (Semiring.toOne.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.semiring (TopologicalRing.toTopologicalSemiring.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) instTopologicalRingRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceToNonUnitalNonAssocRingToNonAssocRingInstRingReal)) (ContinuousMap.algebra.{0, 0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (CommMonoidWithZero.toZero.{0} Real (CommGroupWithZero.toCommMonoidWithZero.{0} Real (Semifield.toCommGroupWithZero.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real (Semiring.toOne.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))))) (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (CommMonoidWithZero.toZero.{0} Real (CommGroupWithZero.toCommMonoidWithZero.{0} Real (Semifield.toCommGroupWithZero.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real (Semiring.toOne.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) Real Real.instCommSemiringReal Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.semiring (Algebra.id.{0} Real Real.instCommSemiringReal) (TopologicalRing.toTopologicalSemiring.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) instTopologicalRingRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceToNonUnitalNonAssocRingToNonAssocRingInstRingReal)) (ContinuousMap.compRightAlgHom.{0, 0, 0, 0} Real Real.instCommSemiringReal Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.semiring (Algebra.id.{0} Real Real.instCommSemiringReal) (TopologicalRing.toTopologicalSemiring.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) instTopologicalRingRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceToNonUnitalNonAssocRingToNonAssocRingInstRingReal) (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (CommMonoidWithZero.toZero.{0} Real (CommGroupWithZero.toCommMonoidWithZero.{0} Real (Semifield.toCommGroupWithZero.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real (Semiring.toOne.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))))) (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) a b)) (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (CommMonoidWithZero.toZero.{0} Real (CommGroupWithZero.toCommMonoidWithZero.{0} Real (Semifield.toCommGroupWithZero.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real (Semiring.toOne.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) a b)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (Homeomorph.toContinuousMap.{0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (CommMonoidWithZero.toZero.{0} Real (CommGroupWithZero.toCommMonoidWithZero.{0} Real (Semifield.toCommGroupWithZero.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real (Semiring.toOne.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))))) (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) a b)) (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (CommMonoidWithZero.toZero.{0} Real (CommGroupWithZero.toCommMonoidWithZero.{0} Real (Semifield.toCommGroupWithZero.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real (Semiring.toOne.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) a b)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (Homeomorph.symm.{0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) a b)) (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (CommMonoidWithZero.toZero.{0} Real (CommGroupWithZero.toCommMonoidWithZero.{0} Real (Semifield.toCommGroupWithZero.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real (Semiring.toOne.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))))) (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) a b)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (CommMonoidWithZero.toZero.{0} Real (CommGroupWithZero.toCommMonoidWithZero.{0} Real (Semifield.toCommGroupWithZero.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real (Semiring.toOne.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (iccHomeoI.{0} Real Real.instLinearOrderedFieldReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instTopologicalRingRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceToNonUnitalNonAssocRingToNonAssocRingInstRingReal a b h)))) (polynomialFunctions.{0} Real Real.instCommSemiringReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (TopologicalRing.toTopologicalSemiring.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) instTopologicalRingRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceToNonUnitalNonAssocRingToNonAssocRingInstRingReal) unitInterval)) (polynomialFunctions.{0} Real Real.instCommSemiringReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (TopologicalRing.toTopologicalSemiring.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) instTopologicalRingRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceToNonUnitalNonAssocRingToNonAssocRingInstRingReal) (Set.Icc.{0} Real Real.instPreorderReal a b))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial_functions.comap_comp_right_alg_hom_Icc_homeo_I polynomialFunctions.comap_compRightAlgHom_iccHomeoIₓ'. -/
 /-- The preimage of polynomials on `[0,1]` under the pullback map by `x ↦ (b-a) * x + a`
 is the polynomials on `[a,b]`. -/

bd15ff41

bump to nightly-2023-05-24-06

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

fbc7b476

Diff

@@ -74,7 +74,7 @@ variable {α : Type _} [TopologicalSpace α] [CommSemiring R] [TopologicalSpace
 lean 3 declaration is
   forall {R : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : CommSemiring.{u1} R] [_inst_3 : TopologicalSpace.{u1} R] [_inst_4 : TopologicalSemiring.{u1} R _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)))] (g : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (f : ContinuousMap.{u2, u1} α R _inst_1 _inst_3) (x : α), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (ContinuousMap.{u2, u1} α R _inst_1 _inst_3) (fun (_x : ContinuousMap.{u2, u1} α R _inst_1 _inst_3) => α -> R) (ContinuousMap.hasCoeToFun.{u2, u1} α R _inst_1 _inst_3) (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ u1) (succ (max u2 u1))} (AlgHom.{u1, u1, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (ContinuousMap.{u2, u1} α R _inst_1 _inst_3) _inst_2 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (ContinuousMap.semiring.{u2, u1} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u1} R _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_2) (Algebra.id.{u1} R _inst_2)) (ContinuousMap.algebra.{u2, u1, u1} α _inst_1 R _inst_2 R _inst_3 (CommSemiring.toSemiring.{u1} R _inst_2) (Algebra.id.{u1} R _inst_2) _inst_4)) (fun (_x : AlgHom.{u1, u1, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (ContinuousMap.{u2, u1} α R _inst_1 _inst_3) _inst_2 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (ContinuousMap.semiring.{u2, u1} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u1} R _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_2) (Algebra.id.{u1} R _inst_2)) (ContinuousMap.algebra.{u2, u1, u1} α _inst_1 R _inst_2 R _inst_3 (CommSemiring.toSemiring.{u1} R _inst_2) (Algebra.id.{u1} R _inst_2) _inst_4)) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) -> (ContinuousMap.{u2, u1} α R _inst_1 _inst_3)) ([anonymous].{u1, u1, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (ContinuousMap.{u2, u1} α R _inst_1 _inst_3) _inst_2 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (ContinuousMap.semiring.{u2, u1} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u1} R _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_2) (Algebra.id.{u1} R _inst_2)) (ContinuousMap.algebra.{u2, u1, u1} α _inst_1 R _inst_2 R _inst_3 (CommSemiring.toSemiring.{u1} R _inst_2) (Algebra.id.{u1} R _inst_2) _inst_4)) (Polynomial.aeval.{u1, max u2 u1} R (ContinuousMap.{u2, u1} α R _inst_1 _inst_3) _inst_2 (ContinuousMap.semiring.{u2, u1} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u1} R _inst_2) _inst_4) (ContinuousMap.algebra.{u2, u1, u1} α _inst_1 R _inst_2 R _inst_3 (CommSemiring.toSemiring.{u1} R _inst_2) (Algebra.id.{u1} R _inst_2) _inst_4) f) g) x) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (ContinuousMap.{u2, u1} α R _inst_1 _inst_3) (fun (_x : ContinuousMap.{u2, u1} α R _inst_1 _inst_3) => α -> R) (ContinuousMap.hasCoeToFun.{u2, u1} α R _inst_1 _inst_3) f x) g)
 but is expected to have type
-  forall {R : Type.{u2}} {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CommSemiring.{u2} R] [_inst_3 : TopologicalSpace.{u2} R] [_inst_4 : TopologicalSemiring.{u2} R _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)))] (g : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (f : ContinuousMap.{u1, u2} α R _inst_1 _inst_3) (x : α), Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => R) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) => ContinuousMap.{u1, u2} α R _inst_1 _inst_3) g) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => R) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u1, u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) => ContinuousMap.{u1, u2} α R _inst_1 _inst_3) g) α R _inst_1 _inst_3 (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} α R _inst_1 _inst_3)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (AlgHom.{u2, u2, max u2 u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) _inst_2 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_2 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2)) (ContinuousMap.algebra.{u1, u2, u2} α _inst_1 R _inst_2 R _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2) _inst_4)) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (fun (_x : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) => ContinuousMap.{u1, u2} α R _inst_1 _inst_3) _x) (SMulHomClass.toFunLike.{max u2 u1, u2, u2, max u2 u1} (AlgHom.{u2, u2, max u2 u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) _inst_2 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_2 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2)) (ContinuousMap.algebra.{u1, u2, u2} α _inst_1 R _inst_2 R _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2) _inst_4)) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) (SMulZeroClass.toSMul.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (AddMonoid.toZero.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2))))))) (DistribSMul.toSMulZeroClass.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R 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_inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) (Semiring.toNonAssocSemiring.{max u2 u1} (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4)))) (Algebra.toModule.{u2, max u2 u1} R (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) _inst_2 (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4) (ContinuousMap.algebra.{u1, u2, u2} α _inst_1 R _inst_2 R _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u2, u2, max u2 u1} (AlgHom.{u2, u2, max u2 u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) _inst_2 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(CommSemiring.toSemiring.{u2} R _inst_2) _inst_4)))) (Algebra.toModule.{u2, max u2 u1} R (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) _inst_2 (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4) (ContinuousMap.algebra.{u1, u2, u2} α _inst_1 R _inst_2 R _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u2, u2, max u2 u1} (AlgHom.{u2, u2, max u2 u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) _inst_2 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_2 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2)) (ContinuousMap.algebra.{u1, u2, u2} α _inst_1 R _inst_2 R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) (Semiring.toNonAssocSemiring.{max u2 u1} (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4)))) (Algebra.toModule.{u2, max u2 u1} R (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) _inst_2 (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4) (ContinuousMap.algebra.{u1, u2, u2} α _inst_1 R _inst_2 R _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, max u2 u1, max u2 u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) _inst_2 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_2 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2)) (ContinuousMap.algebra.{u1, u2, u2} α _inst_1 R _inst_2 R _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2) _inst_4) (AlgHom.{u2, u2, max u2 u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) _inst_2 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_2 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2)) (ContinuousMap.algebra.{u1, u2, u2} α _inst_1 R _inst_2 R _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2) _inst_4)) (AlgHom.algHomClass.{u2, u2, max u2 u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) _inst_2 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_2 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2)) (ContinuousMap.algebra.{u1, u2, u2} α _inst_1 R _inst_2 R _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2) _inst_4)))))) (Polynomial.aeval.{u2, max u2 u1} R (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) _inst_2 (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4) (ContinuousMap.algebra.{u1, u2, u2} α _inst_1 R _inst_2 R _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2) _inst_4) f) g) x) (Polynomial.eval.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => R) x) (CommSemiring.toSemiring.{u2} R _inst_2) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => R) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u1, u2} (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) α R _inst_1 _inst_3 (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} α R _inst_1 _inst_3)) f x) g)
+  forall {R : Type.{u2}} {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CommSemiring.{u2} R] [_inst_3 : TopologicalSpace.{u2} R] [_inst_4 : TopologicalSemiring.{u2} R _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)))] (g : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (f : ContinuousMap.{u1, u2} α R _inst_1 _inst_3) (x : α), Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => R) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) => ContinuousMap.{u1, u2} α R _inst_1 _inst_3) g) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => R) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u1, u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) => ContinuousMap.{u1, u2} α R _inst_1 _inst_3) g) α R _inst_1 _inst_3 (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} α R _inst_1 _inst_3)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (AlgHom.{u2, u2, max u2 u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) _inst_2 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_2 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2)) (ContinuousMap.algebra.{u1, u2, u2} α _inst_1 R _inst_2 R _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2) _inst_4)) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (fun (_x : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) => ContinuousMap.{u1, u2} α R _inst_1 _inst_3) _x) (SMulHomClass.toFunLike.{max u2 u1, u2, u2, max u2 u1} (AlgHom.{u2, u2, max u2 u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) _inst_2 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_2 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2)) (ContinuousMap.algebra.{u1, u2, u2} α _inst_1 R _inst_2 R _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2) _inst_4)) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) (SMulZeroClass.toSMul.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (AddMonoid.toZero.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2))))))) (DistribSMul.toSMulZeroClass.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R 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(CommSemiring.toSemiring.{u2} R _inst_2) _inst_4)))) (Algebra.toModule.{u2, max u2 u1} R (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) _inst_2 (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4) (ContinuousMap.algebra.{u1, u2, u2} α _inst_1 R _inst_2 R _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u2, u2, max u2 u1} (AlgHom.{u2, u2, max u2 u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) _inst_2 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_2 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2)) (ContinuousMap.algebra.{u1, u2, u2} α _inst_1 R _inst_2 R _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2) _inst_4)) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) (Semiring.toNonAssocSemiring.{max u2 u1} (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{u2} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) _inst_2 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_2 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2)))) (Module.toDistribMulAction.{u2, max u2 u1} R (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) (Semiring.toNonAssocSemiring.{max u2 u1} (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4)))) (Algebra.toModule.{u2, max u2 u1} R (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) _inst_2 (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4) (ContinuousMap.algebra.{u1, u2, u2} α _inst_1 R _inst_2 R _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, max u2 u1, max u2 u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) _inst_2 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_2 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2)) (ContinuousMap.algebra.{u1, u2, u2} α _inst_1 R _inst_2 R _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2) _inst_4) (AlgHom.{u2, u2, max u2 u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) _inst_2 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_2 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2)) (ContinuousMap.algebra.{u1, u2, u2} α _inst_1 R _inst_2 R _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2) _inst_4)) (AlgHom.algHomClass.{u2, u2, max u2 u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) _inst_2 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_2 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2)) (ContinuousMap.algebra.{u1, u2, u2} α _inst_1 R _inst_2 R _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2) _inst_4)))))) (Polynomial.aeval.{u2, max u2 u1} R (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) _inst_2 (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4) (ContinuousMap.algebra.{u1, u2, u2} α _inst_1 R _inst_2 R _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2) _inst_4) f) g) x) (Polynomial.eval.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => R) x) (CommSemiring.toSemiring.{u2} R _inst_2) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => R) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u1, u2} (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) α R _inst_1 _inst_3 (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} α R _inst_1 _inst_3)) f x) g)
 Case conversion may be inaccurate. Consider using '#align polynomial.aeval_continuous_map_apply Polynomial.aeval_continuousMap_applyₓ'. -/
 @[simp]
 theorem aeval_continuousMap_apply (g : R[X]) (f : C(α, R)) (x : α) :
@@ -185,7 +185,7 @@ def polynomialFunctions (X : Set R) : Subalgebra R C(X, R) :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSemiring.{u1} R _inst_2 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))] (X : Set.{u1} R), Eq.{succ u1} (Set.{u1} (ContinuousMap.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} R) Type.{u1} (Set.hasCoeToSort.{u1} R) X) R (Subtype.topologicalSpace.{u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Set.{u1} R) (Set.hasMem.{u1} R) x X) _inst_2) _inst_2)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subalgebra.{u1, u1} R (ContinuousMap.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} R) Type.{u1} (Set.hasCoeToSort.{u1} R) X) R (Subtype.topologicalSpace.{u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Set.{u1} R) (Set.hasMem.{u1} R) x X) _inst_2) _inst_2) _inst_1 (ContinuousMap.semiring.{u1, u1} (coeSort.{succ u1, succ (succ u1)} 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 but is expected to have type
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R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3)))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (AddMonoid.toAddZeroClass.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (AddCommMonoid.toAddMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3)))))) (DistribMulAction.toDistribSMul.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3))))) (Module.toDistribMulAction.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3)))) (Algebra.toModule.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3)))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3)))) (Algebra.toModule.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3)))) (Algebra.toModule.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3) (AlgHom.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3)) (AlgHom.algHomClass.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3)))))) (Polynomial.toContinuousMapOnAlgHom.{u1} R _inst_1 _inst_2 _inst_3 X)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSemiring.{u1} R _inst_2 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))] (X : Set.{u1} R), Eq.{succ u1} (Set.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2)) (SetLike.coe.{u1, u1} (Subalgebra.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Subalgebra.instSetLikeSubalgebra.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3)) (polynomialFunctions.{u1} R _inst_1 _inst_2 _inst_3 X)) (Set.range.{u1, succ u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgHom.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (AddMonoid.toZero.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (AddCommMonoid.toAddMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3)))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (AddMonoid.toAddZeroClass.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (AddCommMonoid.toAddMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3)))))) (DistribMulAction.toDistribSMul.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3))))) (Module.toDistribMulAction.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3)))) (Algebra.toModule.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3)))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3)))) (Algebra.toModule.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3)))) (Algebra.toModule.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) 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(Algebra.id.{u1} R _inst_1)) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3)) (AlgHom.algHomClass.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3)))))) (Polynomial.toContinuousMapOnAlgHom.{u1} R _inst_1 _inst_2 _inst_3 X)))
 Case conversion may be inaccurate. Consider using '#align polynomial_functions_coe polynomialFunctions_coeₓ'. -/
 @[simp]
 theorem polynomialFunctions_coe (X : Set R) :

bd15ff41

bump to nightly-2023-05-13-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/403190b5419b3f03f1a2893ad9352ca7f7d8bff6

d312d6d5

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 
 ! This file was ported from Lean 3 source module topology.continuous_function.polynomial
-! leanprover-community/mathlib commit a148d797a1094ab554ad4183a4ad6f130358ef64
+! leanprover-community/mathlib commit bd15ff41b70f5e2cc210f26f25a8d5c53b20d3de
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Topology.UnitInterval
 /-!
 # Constructions relating polynomial functions and continuous functions.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 ## Main definitions
 
 * `polynomial.to_continuous_map_on p X`: for `X : set R`, interprets a polynomial `p`

a148d797

bump to nightly-2023-05-11-12

mathlib commit https://github.com/leanprover-community/mathlib/commit/28b2a92f2996d28e580450863c130955de0ed398

a36e0ba2

Diff

@@ -37,6 +37,7 @@ section
 
 variable [Semiring R] [TopologicalSpace R] [TopologicalSemiring R]
 
+#print Polynomial.toContinuousMap /-
 /--
 Every polynomial with coefficients in a topological semiring gives a (bundled) continuous function.
 -/
@@ -44,7 +45,9 @@ Every polynomial with coefficients in a topological semiring gives a (bundled) c
 def toContinuousMap (p : R[X]) : C(R, R) :=
   ⟨fun x : R => p.eval x, by continuity⟩
 #align polynomial.to_continuous_map Polynomial.toContinuousMap
+-/
 
+#print Polynomial.toContinuousMapOn /-
 /-- A polynomial as a continuous function,
 with domain restricted to some subset of the semiring of coefficients.
 
@@ -54,6 +57,7 @@ with domain restricted to some subset of the semiring of coefficients.
 def toContinuousMapOn (p : R[X]) (X : Set R) : C(X, R) :=
   ⟨fun x : X => p.toContinuousMap x, by continuity⟩
 #align polynomial.to_continuous_map_on Polynomial.toContinuousMapOn
+-/
 
 -- TODO some lemmas about when `to_continuous_map_on` is injective?
 end
@@ -63,6 +67,12 @@ section
 variable {α : Type _} [TopologicalSpace α] [CommSemiring R] [TopologicalSpace R]
   [TopologicalSemiring R]
 
+/- warning: polynomial.aeval_continuous_map_apply -> Polynomial.aeval_continuousMap_apply is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(ContinuousMap.{u1, u2} α R _inst_1 _inst_3) (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4)))))) (DistribMulAction.toDistribSMul.{u2, max u2 u1} R (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2))) (AddCommMonoid.toAddMonoid.{max u2 u1} (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) (Semiring.toNonAssocSemiring.{max u2 u1} (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4))))) (Module.toDistribMulAction.{u2, max u2 u1} R (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) (CommSemiring.toSemiring.{u2} R 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(CommSemiring.toSemiring.{u2} R _inst_2) _inst_4)))) (Algebra.toModule.{u2, max u2 u1} R (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) _inst_2 (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4) (ContinuousMap.algebra.{u1, u2, u2} α _inst_1 R _inst_2 R _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u2, u2, max u2 u1} (AlgHom.{u2, u2, max u2 u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) _inst_2 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_2 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2)) (ContinuousMap.algebra.{u1, u2, u2} α _inst_1 R _inst_2 R _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2) _inst_4)) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) (Semiring.toNonAssocSemiring.{max u2 u1} (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{u2} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) _inst_2 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_2 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2)))) (Module.toDistribMulAction.{u2, max u2 u1} R (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) (Semiring.toNonAssocSemiring.{max u2 u1} (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4)))) (Algebra.toModule.{u2, max u2 u1} R (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) _inst_2 (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4) (ContinuousMap.algebra.{u1, u2, u2} α _inst_1 R _inst_2 R _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, max u2 u1, max u2 u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) _inst_2 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_2 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2)) (ContinuousMap.algebra.{u1, u2, u2} α _inst_1 R _inst_2 R _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2) _inst_4) (AlgHom.{u2, u2, max u2 u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) _inst_2 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_2 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2)) (ContinuousMap.algebra.{u1, u2, u2} α _inst_1 R _inst_2 R _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2) _inst_4)) (AlgHom.algHomClass.{u2, u2, max u2 u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) _inst_2 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_2 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2)) (ContinuousMap.algebra.{u1, u2, u2} α _inst_1 R _inst_2 R _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2) _inst_4)))))) (Polynomial.aeval.{u2, max u2 u1} R (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) _inst_2 (ContinuousMap.instSemiringContinuousMap.{u1, u2} α R _inst_1 _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) _inst_4) (ContinuousMap.algebra.{u1, u2, u2} α _inst_1 R _inst_2 R _inst_3 (CommSemiring.toSemiring.{u2} R _inst_2) (Algebra.id.{u2} R _inst_2) _inst_4) f) g) x) (Polynomial.eval.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => R) x) (CommSemiring.toSemiring.{u2} R _inst_2) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => R) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u1, u2} (ContinuousMap.{u1, u2} α R _inst_1 _inst_3) α R _inst_1 _inst_3 (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} α R _inst_1 _inst_3)) f x) g)
+Case conversion may be inaccurate. Consider using '#align polynomial.aeval_continuous_map_apply Polynomial.aeval_continuousMap_applyₓ'. -/
 @[simp]
 theorem aeval_continuousMap_apply (g : R[X]) (f : C(α, R)) (x : α) :
     ((Polynomial.aeval f) g) x = g.eval (f x) :=
@@ -82,6 +92,12 @@ noncomputable section
 
 variable [CommSemiring R] [TopologicalSpace R] [TopologicalSemiring R]
 
+/- warning: polynomial.to_continuous_map_alg_hom -> Polynomial.toContinuousMapAlgHom 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 polynomial.to_continuous_map_alg_hom Polynomial.toContinuousMapAlgHomₓ'. -/
 /-- The algebra map from `R[X]` to continuous functions `C(R, R)`.
 -/
 @[simps]
@@ -108,6 +124,12 @@ def toContinuousMapAlgHom : R[X] →ₐ[R] C(R, R)
     simp [Algebra.algebraMap_eq_smul_one]
 #align polynomial.to_continuous_map_alg_hom Polynomial.toContinuousMapAlgHom
 
+/- warning: polynomial.to_continuous_map_on_alg_hom -> Polynomial.toContinuousMapOnAlgHom is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.to_continuous_map_on_alg_hom Polynomial.toContinuousMapOnAlgHomₓ'. -/
 /-- The algebra map from `R[X]` to continuous functions `C(X, R)`, for any subset `X` of `R`.
 -/
 @[simps]
@@ -142,6 +164,12 @@ section
 
 variable [CommSemiring R] [TopologicalSpace R] [TopologicalSemiring R]
 
+/- warning: polynomial_functions -> polynomialFunctions is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial_functions polynomialFunctionsₓ'. -/
 /--
 The subalgebra of polynomial functions in `C(X, R)`, for `X` a subset of some topological semiring
 `R`.
@@ -150,6 +178,12 @@ def polynomialFunctions (X : Set R) : Subalgebra R C(X, R) :=
   (⊤ : Subalgebra R R[X]).map (Polynomial.toContinuousMapOnAlgHom X)
 #align polynomial_functions polynomialFunctions
 
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+but is expected to have type
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(CommSemiring.toSemiring.{u1} R _inst_1) _inst_3)))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (AddMonoid.toAddZeroClass.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (AddCommMonoid.toAddMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3)))))) (DistribMulAction.toDistribSMul.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3))))) (Module.toDistribMulAction.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3)))) (Algebra.toModule.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3)))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3)))) (Algebra.toModule.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (Semiring.toNonAssocSemiring.{u1} (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3)))) (Algebra.toModule.{u1, u1} R (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3) (AlgHom.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3)) (AlgHom.algHomClass.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ContinuousMap.instSemiringContinuousMap.{u1, u1} (Set.Elem.{u1} R X) R (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) (ContinuousMap.algebra.{u1, u1, u1} (Set.Elem.{u1} R X) (instTopologicalSpaceSubtype.{u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x X) _inst_2) R _inst_1 R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) _inst_3)))))) (Polynomial.toContinuousMapOnAlgHom.{u1} R _inst_1 _inst_2 _inst_3 X)))
+Case conversion may be inaccurate. Consider using '#align polynomial_functions_coe polynomialFunctions_coeₓ'. -/
 @[simp]
 theorem polynomialFunctions_coe (X : Set R) :
     (polynomialFunctions X : Set C(X, R)) = Set.range (Polynomial.toContinuousMapOnAlgHom X) :=
@@ -158,6 +192,7 @@ theorem polynomialFunctions_coe (X : Set R) :
   simp [polynomialFunctions]
 #align polynomial_functions_coe polynomialFunctions_coe
 
+#print polynomialFunctions_separatesPoints /-
 -- TODO:
 -- if `f : R → R` is an affine equivalence, then pulling back along `f`
 -- induces a normed algebra isomorphism between `polynomial_functions X` and
@@ -170,11 +205,18 @@ theorem polynomialFunctions_separatesPoints (X : Set R) : (polynomialFunctions X
   dsimp; simp only [Polynomial.eval_X]
   exact fun h' => h (Subtype.ext h')
 #align polynomial_functions_separates_points polynomialFunctions_separatesPoints
+-/
 
 open unitInterval
 
 open ContinuousMap
 
+/- warning: polynomial_functions.comap_comp_right_alg_hom_Icc_homeo_I -> polynomialFunctions.comap_compRightAlgHom_iccHomeoI is a dubious translation:
+lean 3 declaration is
+  forall (a : Real) (b : Real) (h : LT.lt.{0} Real Real.hasLt a b), Eq.{1} (Subalgebra.{0, 0} Real (ContinuousMap.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) a b)) Real (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) a b)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) Real.commSemiring (ContinuousMap.semiring.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) a b)) Real (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) a b)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.semiring (TopologicalRing.to_topologicalSemiring.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) Real.topologicalRing)) (ContinuousMap.algebra.{0, 0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) a b)) (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) a b)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) Real Real.commSemiring Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.semiring (Algebra.id.{0} Real Real.commSemiring) (TopologicalRing.to_topologicalSemiring.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) Real.topologicalRing))) (Subalgebra.comap.{0, 0, 0} Real (ContinuousMap.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) a b)) Real (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real 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(UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) Real.topologicalRing)) (ContinuousMap.algebra.{0, 0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) a b)) (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) a b)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) Real Real.commSemiring Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.semiring (Algebra.id.{0} Real Real.commSemiring) (TopologicalRing.to_topologicalSemiring.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) Real.topologicalRing)) (ContinuousMap.semiring.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} 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(LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) a b)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (Homeomorph.toContinuousMap.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real (StrictOrderedRing.toRing.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real (AddMonoidWithOne.toOne.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (AddCommGroupWithOne.toAddGroupWithOne.{0} Real (Ring.toAddCommGroupWithOne.{0} Real (StrictOrderedRing.toRing.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))))))))))) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) a b)) (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real (StrictOrderedRing.toRing.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real (AddMonoidWithOne.toOne.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (AddCommGroupWithOne.toAddGroupWithOne.{0} Real (Ring.toAddCommGroupWithOne.{0} Real (StrictOrderedRing.toRing.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))))))))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) a b)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (Homeomorph.symm.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) a b)) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real (StrictOrderedRing.toRing.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real (AddMonoidWithOne.toOne.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (AddCommGroupWithOne.toAddGroupWithOne.{0} Real (Ring.toAddCommGroupWithOne.{0} Real (StrictOrderedRing.toRing.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))))))))))) (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) a b)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommGroup.toPartialOrder.{0} Real (StrictOrderedRing.toOrderedAddCommGroup.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real (StrictOrderedRing.toRing.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField)))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real (AddMonoidWithOne.toOne.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (AddCommGroupWithOne.toAddGroupWithOne.{0} Real (Ring.toAddCommGroupWithOne.{0} Real (StrictOrderedRing.toRing.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))))))))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (iccHomeoI.{0} Real Real.linearOrderedField (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.topologicalRing a b h)))) (polynomialFunctions.{0} Real Real.commSemiring (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (TopologicalRing.to_topologicalSemiring.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) Real.topologicalRing) unitInterval)) (polynomialFunctions.{0} Real Real.commSemiring (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (TopologicalRing.to_topologicalSemiring.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) Real.topologicalRing) (Set.Icc.{0} Real Real.preorder a b))
+but is expected to have type
+  forall (a : Real) (b : Real) (h : LT.lt.{0} Real Real.instLTReal a b), Eq.{1} (Subalgebra.{0, 0} Real (ContinuousMap.{0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) a b)) Real (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) a b)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) Real.instCommSemiringReal (ContinuousMap.instSemiringContinuousMap.{0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) a b)) Real (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) a b)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.semiring (TopologicalRing.toTopologicalSemiring.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) instTopologicalRingRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceToNonUnitalNonAssocRingToNonAssocRingInstRingReal)) (ContinuousMap.algebra.{0, 0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) a b)) (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) a b)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) Real Real.instCommSemiringReal Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.semiring (Algebra.id.{0} Real Real.instCommSemiringReal) (TopologicalRing.toTopologicalSemiring.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) instTopologicalRingRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceToNonUnitalNonAssocRingToNonAssocRingInstRingReal))) (Subalgebra.comap.{0, 0, 0} Real (ContinuousMap.{0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) a b)) Real (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) a b)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (ContinuousMap.{0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (CommMonoidWithZero.toZero.{0} Real (CommGroupWithZero.toCommMonoidWithZero.{0} Real (Semifield.toCommGroupWithZero.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real (Semiring.toOne.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))))) Real (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (CommMonoidWithZero.toZero.{0} Real (CommGroupWithZero.toCommMonoidWithZero.{0} Real (Semifield.toCommGroupWithZero.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real (Semiring.toOne.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) Real.instCommSemiringReal (ContinuousMap.instSemiringContinuousMap.{0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) a b)) Real (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) a b)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.semiring (TopologicalRing.toTopologicalSemiring.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) instTopologicalRingRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceToNonUnitalNonAssocRingToNonAssocRingInstRingReal)) (ContinuousMap.algebra.{0, 0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) a b)) (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) a b)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) Real Real.instCommSemiringReal Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.semiring (Algebra.id.{0} Real Real.instCommSemiringReal) (TopologicalRing.toTopologicalSemiring.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) instTopologicalRingRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceToNonUnitalNonAssocRingToNonAssocRingInstRingReal)) (ContinuousMap.instSemiringContinuousMap.{0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (CommMonoidWithZero.toZero.{0} Real (CommGroupWithZero.toCommMonoidWithZero.{0} Real (Semifield.toCommGroupWithZero.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real (Semiring.toOne.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))))) Real (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (CommMonoidWithZero.toZero.{0} Real (CommGroupWithZero.toCommMonoidWithZero.{0} Real (Semifield.toCommGroupWithZero.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real (Semiring.toOne.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.semiring (TopologicalRing.toTopologicalSemiring.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) instTopologicalRingRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceToNonUnitalNonAssocRingToNonAssocRingInstRingReal)) (ContinuousMap.algebra.{0, 0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (CommMonoidWithZero.toZero.{0} Real (CommGroupWithZero.toCommMonoidWithZero.{0} Real (Semifield.toCommGroupWithZero.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real (Semiring.toOne.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))))) (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (CommMonoidWithZero.toZero.{0} Real (CommGroupWithZero.toCommMonoidWithZero.{0} Real (Semifield.toCommGroupWithZero.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real (Semiring.toOne.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) Real Real.instCommSemiringReal Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.semiring (Algebra.id.{0} Real Real.instCommSemiringReal) (TopologicalRing.toTopologicalSemiring.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) instTopologicalRingRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceToNonUnitalNonAssocRingToNonAssocRingInstRingReal)) (ContinuousMap.compRightAlgHom.{0, 0, 0, 0} Real Real.instCommSemiringReal Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.semiring (Algebra.id.{0} Real Real.instCommSemiringReal) (TopologicalRing.toTopologicalSemiring.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) instTopologicalRingRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceToNonUnitalNonAssocRingToNonAssocRingInstRingReal) (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (CommMonoidWithZero.toZero.{0} Real (CommGroupWithZero.toCommMonoidWithZero.{0} Real (Semifield.toCommGroupWithZero.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real (Semiring.toOne.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))))) (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) a b)) (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (CommMonoidWithZero.toZero.{0} Real (CommGroupWithZero.toCommMonoidWithZero.{0} Real (Semifield.toCommGroupWithZero.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real (Semiring.toOne.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) a b)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (Homeomorph.toContinuousMap.{0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (CommMonoidWithZero.toZero.{0} Real (CommGroupWithZero.toCommMonoidWithZero.{0} Real (Semifield.toCommGroupWithZero.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real (Semiring.toOne.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))))) (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) a b)) (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (CommMonoidWithZero.toZero.{0} Real (CommGroupWithZero.toCommMonoidWithZero.{0} Real (Semifield.toCommGroupWithZero.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real (Semiring.toOne.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) a b)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (Homeomorph.symm.{0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) a b)) (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (CommMonoidWithZero.toZero.{0} Real (CommGroupWithZero.toCommMonoidWithZero.{0} Real (Semifield.toCommGroupWithZero.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real (Semiring.toOne.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))))) (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) a b)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (StrictOrderedRing.toPartialOrder.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (CommMonoidWithZero.toZero.{0} Real (CommGroupWithZero.toCommMonoidWithZero.{0} Real (Semifield.toCommGroupWithZero.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real (Semiring.toOne.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (LinearOrderedSemifield.toSemifield.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (iccHomeoI.{0} Real Real.instLinearOrderedFieldReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instTopologicalRingRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceToNonUnitalNonAssocRingToNonAssocRingInstRingReal a b h)))) (polynomialFunctions.{0} Real Real.instCommSemiringReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (TopologicalRing.toTopologicalSemiring.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) instTopologicalRingRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceToNonUnitalNonAssocRingToNonAssocRingInstRingReal) unitInterval)) (polynomialFunctions.{0} Real Real.instCommSemiringReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (TopologicalRing.toTopologicalSemiring.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) instTopologicalRingRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceToNonUnitalNonAssocRingToNonAssocRingInstRingReal) (Set.Icc.{0} Real Real.instPreorderReal a b))
+Case conversion may be inaccurate. Consider using '#align polynomial_functions.comap_comp_right_alg_hom_Icc_homeo_I polynomialFunctions.comap_compRightAlgHom_iccHomeoIₓ'. -/
 /-- The preimage of polynomials on `[0,1]` under the pullback map by `x ↦ (b-a) * x + a`
 is the polynomials on `[a,b]`. -/
 theorem polynomialFunctions.comap_compRightAlgHom_iccHomeoI (a b : ℝ) (h : a < b) :

a148d797

bump to nightly-2023-03-08-14

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

f7af4b63

Diff

@@ -167,7 +167,7 @@ theorem polynomialFunctions_separatesPoints (X : Set R) : (polynomialFunctions X
   by
   -- We use `polynomial.X`, then clean up.
   refine' ⟨_, ⟨⟨_, ⟨⟨Polynomial.X, ⟨Algebra.mem_top, rfl⟩⟩, rfl⟩⟩, _⟩⟩
-  dsimp; simp only [Polynomial.eval_x]
+  dsimp; simp only [Polynomial.eval_X]
   exact fun h' => h (Subtype.ext h')
 #align polynomial_functions_separates_points polynomialFunctions_separatesPoints
 
@@ -190,8 +190,8 @@ theorem polynomialFunctions.comap_compRightAlgHom_iccHomeoI (a b : ℝ) (h : a <
     refine' ⟨q, ⟨_, _⟩⟩
     · simp
     · ext x
-      simp only [neg_mul, RingHom.map_neg, RingHom.map_mul, AlgHom.coe_toRingHom, Polynomial.eval_x,
-        Polynomial.eval_neg, Polynomial.eval_c, Polynomial.eval_smul, smul_eq_mul,
+      simp only [neg_mul, RingHom.map_neg, RingHom.map_mul, AlgHom.coe_toRingHom, Polynomial.eval_X,
+        Polynomial.eval_neg, Polynomial.eval_C, Polynomial.eval_smul, smul_eq_mul,
         Polynomial.eval_mul, Polynomial.eval_add, Polynomial.coe_aeval_eq_eval,
         Polynomial.eval_comp, Polynomial.toContinuousMapOnAlgHom_apply,
         Polynomial.toContinuousMapOn_apply, Polynomial.toContinuousMap_apply]

a148d797

bump to nightly-2023-03-08-10

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

422cc012

Diff

@@ -166,7 +166,7 @@ theorem polynomialFunctions_separatesPoints (X : Set R) : (polynomialFunctions X
   fun x y h =>
   by
   -- We use `polynomial.X`, then clean up.
-  refine' ⟨_, ⟨⟨_, ⟨⟨Polynomial.x, ⟨Algebra.mem_top, rfl⟩⟩, rfl⟩⟩, _⟩⟩
+  refine' ⟨_, ⟨⟨_, ⟨⟨Polynomial.X, ⟨Algebra.mem_top, rfl⟩⟩, rfl⟩⟩, _⟩⟩
   dsimp; simp only [Polynomial.eval_x]
   exact fun h' => h (Subtype.ext h')
 #align polynomial_functions_separates_points polynomialFunctions_separatesPoints
@@ -186,7 +186,7 @@ theorem polynomialFunctions.comap_compRightAlgHom_iccHomeoI (a b : ℝ) (h : a <
   · rintro ⟨p, ⟨-, w⟩⟩
     rw [FunLike.ext_iff] at w
     dsimp at w
-    let q := p.comp ((b - a)⁻¹ • Polynomial.x + Polynomial.c (-a * (b - a)⁻¹))
+    let q := p.comp ((b - a)⁻¹ • Polynomial.X + Polynomial.C (-a * (b - a)⁻¹))
     refine' ⟨q, ⟨_, _⟩⟩
     · simp
     · ext x
@@ -214,7 +214,7 @@ theorem polynomialFunctions.comap_compRightAlgHom_iccHomeoI (a b : ℝ) (h : a <
         · rw [← div_eq_mul_inv, div_le_one (sub_pos.mpr h)]
           exact w₃
   · rintro ⟨p, ⟨-, rfl⟩⟩
-    let q := p.comp ((b - a) • Polynomial.x + Polynomial.c a)
+    let q := p.comp ((b - a) • Polynomial.X + Polynomial.C a)
     refine' ⟨q, ⟨_, _⟩⟩
     · simp
     · ext x

a148d797

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

a148d797

chore: rename StarSubalgebra.adjoin to StarAlgebra.adjoin (#11339)

This makes it consistent with all the other adjoin in the library

2b6a6f13

Diff

@@ -227,7 +227,7 @@ theorem polynomialFunctions.le_equalizer {A : Type*} [Semiring A] [Algebra R A]
   rw [polynomialFunctions.eq_adjoin_X s]
   exact φ.adjoin_le_equalizer ψ fun x hx => (Set.mem_singleton_iff.1 hx).symm ▸ h
 
-open StarSubalgebra
+open StarAlgebra
 
 theorem polynomialFunctions.starClosure_eq_adjoin_X [StarRing R] [ContinuousStar R] (s : Set R) :
     (polynomialFunctions s).starClosure = adjoin R {toContinuousMapOnAlgHom s X} := by

a148d797

change the order of operation in zsmulRec and nsmulRec (#11451)

We change the following field in the definition of an additive commutative monoid:

 nsmul_succ : ∀ (n : ℕ) (x : G),
-  AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+  AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x

where the latter is more natural

We adjust the definitions of ^ in monoids, groups, etc. Originally there was a warning comment about why this natural order was preferred

use x * npowRec n x and not npowRec n x * x in the definition to make sure that definitional unfolding of npowRec is blocked, to avoid deep recursion issues.

but it seems to no longer apply.

Remarks on the PR :

pow_succ and pow_succ' have switched their meanings.
Most of the time, the proofs were adjusted by priming/unpriming one lemma, or exchanging left and right; a few proofs were more complicated to adjust.
In particular, [Mathlib/NumberTheory/RamificationInertia.lean] used Ideal.IsPrime.mul_mem_pow which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul.
the docstring for Cauchy condensation test in [Mathlib/Analysis/PSeries.lean] was mathematically incorrect, I added the mention that the function is antitone.

9a3feeae

Diff

@@ -217,7 +217,7 @@ theorem polynomialFunctions.eq_adjoin_X (s : Set R) :
     exact Subalgebra.algebraMap_mem _ r
   · rw [map_add]
     exact add_mem hf hg
-  · rw [pow_succ', ← mul_assoc, map_mul]
+  · rw [pow_succ, ← mul_assoc, map_mul]
     exact mul_mem hn (Algebra.subset_adjoin <| Set.mem_singleton _)
 
 theorem polynomialFunctions.le_equalizer {A : Type*} [Semiring A] [Algebra R A] (s : Set R)

a148d797

chore: more backporting of simp changes from #10995 (#11001)

Co-authored-by: Patrick Massot <patrickmassot@free.fr> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

d9589c14

Diff

@@ -176,9 +176,9 @@ theorem polynomialFunctions.comap_compRightAlgHom_iccHomeoI (a b : ℝ) (h : a <
     refine' ⟨q, ⟨_, _⟩⟩
     · simp
     · ext x
-      simp only [neg_mul, RingHom.map_neg, RingHom.map_mul, AlgHom.coe_toRingHom, Polynomial.eval_X,
-        Polynomial.eval_neg, Polynomial.eval_C, Polynomial.eval_smul, smul_eq_mul,
-        Polynomial.eval_mul, Polynomial.eval_add, Polynomial.coe_aeval_eq_eval,
+      simp only [q, neg_mul, RingHom.map_neg, RingHom.map_mul, AlgHom.coe_toRingHom,
+        Polynomial.eval_X, Polynomial.eval_neg, Polynomial.eval_C, Polynomial.eval_smul,
+        smul_eq_mul, Polynomial.eval_mul, Polynomial.eval_add, Polynomial.coe_aeval_eq_eval,
         Polynomial.eval_comp, Polynomial.toContinuousMapOnAlgHom_apply,
         Polynomial.toContinuousMapOn_apply, Polynomial.toContinuousMap_apply]
       convert w ⟨_, _⟩
@@ -202,7 +202,7 @@ theorem polynomialFunctions.comap_compRightAlgHom_iccHomeoI (a b : ℝ) (h : a <
     refine' ⟨q, ⟨_, _⟩⟩
     · simp
     · ext x
-      simp [mul_comm]
+      simp [q, mul_comm]
 set_option linter.uppercaseLean3 false in
 #align polynomial_functions.comap_comp_right_alg_hom_Icc_homeo_I polynomialFunctions.comap_compRightAlgHom_iccHomeoI

a148d797

chore: reduce imports (#9830)

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

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

f4c4ca61

Diff

@@ -4,9 +4,9 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
 import Mathlib.Topology.Algebra.Polynomial
-import Mathlib.Topology.Algebra.StarSubalgebra
 import Mathlib.Topology.ContinuousFunction.Algebra
 import Mathlib.Topology.UnitInterval
+import Mathlib.Algebra.Star.Subalgebra
 
 #align_import topology.continuous_function.polynomial from "leanprover-community/mathlib"@"a148d797a1094ab554ad4183a4ad6f130358ef64"

a148d797

chore(*): rename FunLike to DFunLike (#9785)

This prepares for the introduction of a non-dependent synonym of FunLike, which helps a lot with keeping #8386 readable.

This is entirely search-and-replace in 680197f combined with manual fixes in 4145626, e900597 and b8428f8. The commands that generated this change:

sed -i 's/\bFunLike\b/DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoFunLike\b/toDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/import Mathlib.Data.DFunLike/import Mathlib.Data.FunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bHom_FunLike\b/Hom_DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean     
sed -i 's/\binstFunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bfunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoo many metavariables to apply `fun_like.has_coe_to_fun`/too many metavariables to apply `DFunLike.hasCoeToFun`/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

82656743

Diff

@@ -170,7 +170,7 @@ theorem polynomialFunctions.comap_compRightAlgHom_iccHomeoI (a b : ℝ) (h : a <
   ext f
   fconstructor
   · rintro ⟨p, ⟨-, w⟩⟩
-    rw [FunLike.ext_iff] at w
+    rw [DFunLike.ext_iff] at w
     dsimp at w
     let q := p.comp ((b - a)⁻¹ • Polynomial.X + Polynomial.C (-a * (b - a)⁻¹))
     refine' ⟨q, ⟨_, _⟩⟩

a148d797

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

@@ -25,7 +25,7 @@ import Mathlib.Topology.UnitInterval
 -/
 
 
-variable {R : Type _}
+variable {R : Type*}
 
 open Polynomial
 
@@ -59,7 +59,7 @@ end
 
 section
 
-variable {α : Type _} [TopologicalSpace α] [CommSemiring R] [TopologicalSpace R]
+variable {α : Type*} [TopologicalSpace α] [CommSemiring R] [TopologicalSpace R]
   [TopologicalSemiring R]
 
 @[simp]
@@ -220,7 +220,7 @@ theorem polynomialFunctions.eq_adjoin_X (s : Set R) :
   · rw [pow_succ', ← mul_assoc, map_mul]
     exact mul_mem hn (Algebra.subset_adjoin <| Set.mem_singleton _)
 
-theorem polynomialFunctions.le_equalizer {A : Type _} [Semiring A] [Algebra R A] (s : Set R)
+theorem polynomialFunctions.le_equalizer {A : Type*} [Semiring A] [Algebra R A] (s : Set R)
     (φ ψ : C(s, R) →ₐ[R] A)
     (h : φ (toContinuousMapOnAlgHom s X) = ψ (toContinuousMapOnAlgHom s X)) :
     polynomialFunctions s ≤ φ.equalizer ψ := by
@@ -233,7 +233,7 @@ theorem polynomialFunctions.starClosure_eq_adjoin_X [StarRing R] [ContinuousStar
     (polynomialFunctions s).starClosure = adjoin R {toContinuousMapOnAlgHom s X} := by
   rw [polynomialFunctions.eq_adjoin_X s, adjoin_eq_starClosure_adjoin]
 
-theorem polynomialFunctions.starClosure_le_equalizer {A : Type _} [StarRing R] [ContinuousStar R]
+theorem polynomialFunctions.starClosure_le_equalizer {A : Type*} [StarRing R] [ContinuousStar R]
     [Semiring A] [StarRing A] [Algebra R A] (s : Set R) (φ ψ : C(s, R) →⋆ₐ[R] A)
     (h : φ (toContinuousMapOnAlgHom s X) = ψ (toContinuousMapOnAlgHom s X)) :
     (polynomialFunctions s).starClosure ≤ StarAlgHom.equalizer φ ψ := by

a148d797

refactor: link the Stone-Weierstrass theorem to the StarSubalgebra API (#5267)

The Stone-Weierstrass theorem, including the version for IsROrC 𝕜, was developed prior to the introduction of StarSubalgebra. As such, in order to prove it, a predicate ConjInvariantSubalgebra was introduced for ℝ-subalgebras of C(X, 𝕜). This refactors the Stone-Weierstrass theorem to instead use the StarSubalgebra API and removes ContinuousMap.ConjInvariantSubalgebra entirely. In addition, we provide a few corollaries concerning polynomial functions which are missing from the library.

6220e1d0

Diff

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
 import Mathlib.Topology.Algebra.Polynomial
+import Mathlib.Topology.Algebra.StarSubalgebra
 import Mathlib.Topology.ContinuousFunction.Algebra
 import Mathlib.Topology.UnitInterval
 
@@ -205,4 +206,38 @@ theorem polynomialFunctions.comap_compRightAlgHom_iccHomeoI (a b : ℝ) (h : a <
 set_option linter.uppercaseLean3 false in
 #align polynomial_functions.comap_comp_right_alg_hom_Icc_homeo_I polynomialFunctions.comap_compRightAlgHom_iccHomeoI
 
+theorem polynomialFunctions.eq_adjoin_X (s : Set R) :
+    polynomialFunctions s = Algebra.adjoin R {toContinuousMapOnAlgHom s X} := by
+  refine le_antisymm ?_
+    (Algebra.adjoin_le fun _ h => ⟨X, trivial, (Set.mem_singleton_iff.1 h).symm⟩)
+  rintro - ⟨p, -, rfl⟩
+  rw [AlgHom.coe_toRingHom]
+  refine p.induction_on (fun r => ?_) (fun f g hf hg => ?_) fun n r hn => ?_
+  · rw [Polynomial.C_eq_algebraMap, AlgHomClass.commutes]
+    exact Subalgebra.algebraMap_mem _ r
+  · rw [map_add]
+    exact add_mem hf hg
+  · rw [pow_succ', ← mul_assoc, map_mul]
+    exact mul_mem hn (Algebra.subset_adjoin <| Set.mem_singleton _)
+
+theorem polynomialFunctions.le_equalizer {A : Type _} [Semiring A] [Algebra R A] (s : Set R)
+    (φ ψ : C(s, R) →ₐ[R] A)
+    (h : φ (toContinuousMapOnAlgHom s X) = ψ (toContinuousMapOnAlgHom s X)) :
+    polynomialFunctions s ≤ φ.equalizer ψ := by
+  rw [polynomialFunctions.eq_adjoin_X s]
+  exact φ.adjoin_le_equalizer ψ fun x hx => (Set.mem_singleton_iff.1 hx).symm ▸ h
+
+open StarSubalgebra
+
+theorem polynomialFunctions.starClosure_eq_adjoin_X [StarRing R] [ContinuousStar R] (s : Set R) :
+    (polynomialFunctions s).starClosure = adjoin R {toContinuousMapOnAlgHom s X} := by
+  rw [polynomialFunctions.eq_adjoin_X s, adjoin_eq_starClosure_adjoin]
+
+theorem polynomialFunctions.starClosure_le_equalizer {A : Type _} [StarRing R] [ContinuousStar R]
+    [Semiring A] [StarRing A] [Algebra R A] (s : Set R) (φ ψ : C(s, R) →⋆ₐ[R] A)
+    (h : φ (toContinuousMapOnAlgHom s X) = ψ (toContinuousMapOnAlgHom s X)) :
+    (polynomialFunctions s).starClosure ≤ StarAlgHom.equalizer φ ψ := by
+  rw [polynomialFunctions.starClosure_eq_adjoin_X s]
+  exact StarAlgHom.adjoin_le_equalizer φ ψ fun x hx => (Set.mem_singleton_iff.1 hx).symm ▸ h
+
 end

a148d797

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) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module topology.continuous_function.polynomial
-! leanprover-community/mathlib commit a148d797a1094ab554ad4183a4ad6f130358ef64
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.Algebra.Polynomial
 import Mathlib.Topology.ContinuousFunction.Algebra
 import Mathlib.Topology.UnitInterval
 
+#align_import topology.continuous_function.polynomial from "leanprover-community/mathlib"@"a148d797a1094ab554ad4183a4ad6f130358ef64"
+
 /-!
 # Constructions relating polynomial functions and continuous functions.

a148d797

feat: port Topology.ContinuousFunction.Polynomial (#3881)

9d9de69d

`topology.continuous_function.polynomial` ⟷ `Mathlib.Topology.ContinuousFunction.Polynomial`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 670

topology.continuous_function.polynomial ⟷ Mathlib.Topology.ContinuousFunction.Polynomial

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 670

`topology.continuous_function.polynomial` ⟷ `Mathlib.Topology.ContinuousFunction.Polynomial`