analysis.convex.contractible
⟷
Mathlib.Analysis.Convex.Contractible
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.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -30,7 +30,7 @@ protected theorem StarConvex.contractibleSpace (h : StarConvex ℝ x s) (hne : s
refine'
(contractible_iff_id_nullhomotopic _).2
⟨⟨x, h.mem hne⟩, ⟨⟨⟨fun p => ⟨p.1.1 • x + (1 - p.1.1) • p.2, _⟩, _⟩, fun x => _, fun x => _⟩⟩⟩
- · exact h p.2.2 p.1.2.1 (sub_nonneg.2 p.1.2.2) (add_sub_cancel'_right _ _)
+ · exact h p.2.2 p.1.2.1 (sub_nonneg.2 p.1.2.2) (add_sub_cancel _ _)
·
exact
((continuous_subtype_val.fst'.smul continuous_const).add
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
-import Mathbin.Analysis.Convex.Star
-import Mathbin.Topology.Homotopy.Contractible
+import Analysis.Convex.Star
+import Topology.Homotopy.Contractible
#align_import analysis.convex.contractible from "leanprover-community/mathlib"@"dbdf71cee7bb20367cb7e37279c08b0c218cf967"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module analysis.convex.contractible
-! leanprover-community/mathlib commit dbdf71cee7bb20367cb7e37279c08b0c218cf967
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Analysis.Convex.Star
import Mathbin.Topology.Homotopy.Contractible
+#align_import analysis.convex.contractible from "leanprover-community/mathlib"@"dbdf71cee7bb20367cb7e37279c08b0c218cf967"
+
/-!
# A convex set is contractible
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -25,6 +25,7 @@ topological space.
variable {E : Type _} [AddCommGroup E] [Module ℝ E] [TopologicalSpace E] [ContinuousAdd E]
[ContinuousSMul ℝ E] {s : Set E} {x : E}
+#print StarConvex.contractibleSpace /-
/-- A non-empty star convex set is a contractible space. -/
protected theorem StarConvex.contractibleSpace (h : StarConvex ℝ x s) (hne : s.Nonempty) :
ContractibleSpace s :=
@@ -42,16 +43,21 @@ protected theorem StarConvex.contractibleSpace (h : StarConvex ℝ x s) (hne : s
· ext1; simp
· ext1; simp
#align star_convex.contractible_space StarConvex.contractibleSpace
+-/
+#print Convex.contractibleSpace /-
/-- A non-empty convex set is a contractible space. -/
protected theorem Convex.contractibleSpace (hs : Convex ℝ s) (hne : s.Nonempty) :
ContractibleSpace s :=
let ⟨x, hx⟩ := hne
(hs.StarConvex hx).ContractibleSpace hne
#align convex.contractible_space Convex.contractibleSpace
+-/
+#print RealTopologicalVectorSpace.contractibleSpace /-
instance (priority := 100) RealTopologicalVectorSpace.contractibleSpace : ContractibleSpace E :=
(Homeomorph.Set.univ E).contractibleSpace_iff.mp <|
convex_univ.ContractibleSpace Set.univ_nonempty
#align real_topological_vector_space.contractible_space RealTopologicalVectorSpace.contractibleSpace
+-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -25,12 +25,6 @@ topological space.
variable {E : Type _} [AddCommGroup E] [Module ℝ E] [TopologicalSpace E] [ContinuousAdd E]
[ContinuousSMul ℝ E] {s : Set E} {x : E}
-/- warning: star_convex.contractible_space -> StarConvex.contractibleSpace is a dubious translation:
-lean 3 declaration is
- forall {E : Type.{u1}} [_inst_1 : AddCommGroup.{u1} E] [_inst_2 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)] [_inst_3 : TopologicalSpace.{u1} E] [_inst_4 : ContinuousAdd.{u1} E _inst_3 (AddZeroClass.toHasAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_1)))))] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_3] {s : Set.{u1} E} {x : E}, (StarConvex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2)))) x s) -> (Set.Nonempty.{u1} E s) -> (ContractibleSpace.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} E) Type.{u1} (Set.hasCoeToSort.{u1} E) s) (Subtype.topologicalSpace.{u1} E (fun (x : E) => Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) x s) _inst_3))
-but is expected to have type
- forall {E : Type.{u1}} [_inst_1 : AddCommGroup.{u1} E] [_inst_2 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)] [_inst_3 : TopologicalSpace.{u1} E] [_inst_4 : ContinuousAdd.{u1} E _inst_3 (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_1)))))] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_3] {s : Set.{u1} E} {x : E}, (StarConvex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2)))) x s) -> (Set.Nonempty.{u1} E s) -> (ContractibleSpace.{u1} (Set.Elem.{u1} E s) (instTopologicalSpaceSubtype.{u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x s) _inst_3))
-Case conversion may be inaccurate. Consider using '#align star_convex.contractible_space StarConvex.contractibleSpaceₓ'. -/
/-- A non-empty star convex set is a contractible space. -/
protected theorem StarConvex.contractibleSpace (h : StarConvex ℝ x s) (hne : s.Nonempty) :
ContractibleSpace s :=
@@ -49,12 +43,6 @@ protected theorem StarConvex.contractibleSpace (h : StarConvex ℝ x s) (hne : s
· ext1; simp
#align star_convex.contractible_space StarConvex.contractibleSpace
-/- warning: convex.contractible_space -> Convex.contractibleSpace is a dubious translation:
-lean 3 declaration is
- forall {E : Type.{u1}} [_inst_1 : AddCommGroup.{u1} E] [_inst_2 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)] [_inst_3 : TopologicalSpace.{u1} E] [_inst_4 : ContinuousAdd.{u1} E _inst_3 (AddZeroClass.toHasAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_1)))))] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_3] {s : Set.{u1} E}, (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2)))) s) -> (Set.Nonempty.{u1} E s) -> (ContractibleSpace.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} E) Type.{u1} (Set.hasCoeToSort.{u1} E) s) (Subtype.topologicalSpace.{u1} E (fun (x : E) => Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) x s) _inst_3))
-but is expected to have type
- forall {E : Type.{u1}} [_inst_1 : AddCommGroup.{u1} E] [_inst_2 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)] [_inst_3 : TopologicalSpace.{u1} E] [_inst_4 : ContinuousAdd.{u1} E _inst_3 (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_1)))))] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_3] {s : Set.{u1} E}, (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2)))) s) -> (Set.Nonempty.{u1} E s) -> (ContractibleSpace.{u1} (Set.Elem.{u1} E s) (instTopologicalSpaceSubtype.{u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x s) _inst_3))
-Case conversion may be inaccurate. Consider using '#align convex.contractible_space Convex.contractibleSpaceₓ'. -/
/-- A non-empty convex set is a contractible space. -/
protected theorem Convex.contractibleSpace (hs : Convex ℝ s) (hne : s.Nonempty) :
ContractibleSpace s :=
@@ -62,12 +50,6 @@ protected theorem Convex.contractibleSpace (hs : Convex ℝ s) (hne : s.Nonempty
(hs.StarConvex hx).ContractibleSpace hne
#align convex.contractible_space Convex.contractibleSpace
-/- warning: real_topological_vector_space.contractible_space -> RealTopologicalVectorSpace.contractibleSpace is a dubious translation:
-lean 3 declaration is
- forall {E : Type.{u1}} [_inst_1 : AddCommGroup.{u1} E] [_inst_2 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)] [_inst_3 : TopologicalSpace.{u1} E] [_inst_4 : ContinuousAdd.{u1} E _inst_3 (AddZeroClass.toHasAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_1)))))] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_3], ContractibleSpace.{u1} E _inst_3
-but is expected to have type
- forall {E : Type.{u1}} [_inst_1 : AddCommGroup.{u1} E] [_inst_2 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)] [_inst_3 : TopologicalSpace.{u1} E] [_inst_4 : ContinuousAdd.{u1} E _inst_3 (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_1)))))] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_3], ContractibleSpace.{u1} E _inst_3
-Case conversion may be inaccurate. Consider using '#align real_topological_vector_space.contractible_space RealTopologicalVectorSpace.contractibleSpaceₓ'. -/
instance (priority := 100) RealTopologicalVectorSpace.contractibleSpace : ContractibleSpace E :=
(Homeomorph.Set.univ E).contractibleSpace_iff.mp <|
convex_univ.ContractibleSpace Set.univ_nonempty
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -45,10 +45,8 @@ protected theorem StarConvex.contractibleSpace (h : StarConvex ℝ x s) (hne : s
((continuous_const.sub continuous_subtype_val.fst').smul
continuous_subtype_val.snd')).subtype_mk
_
- · ext1
- simp
- · ext1
- simp
+ · ext1; simp
+ · ext1; simp
#align star_convex.contractible_space StarConvex.contractibleSpace
/- warning: convex.contractible_space -> Convex.contractibleSpace is a dubious translation:
mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
! This file was ported from Lean 3 source module analysis.convex.contractible
-! leanprover-community/mathlib commit 3339976e2bcae9f1c81e620836d1eb736e3c4700
+! leanprover-community/mathlib commit dbdf71cee7bb20367cb7e37279c08b0c218cf967
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -14,6 +14,9 @@ import Mathbin.Topology.Homotopy.Contractible
/-!
# A convex set is contractible
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
In this file we prove that a (star) convex set in a real topological vector space is a contractible
topological space.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee
@@ -22,6 +22,12 @@ topological space.
variable {E : Type _} [AddCommGroup E] [Module ℝ E] [TopologicalSpace E] [ContinuousAdd E]
[ContinuousSMul ℝ E] {s : Set E} {x : E}
+/- warning: star_convex.contractible_space -> StarConvex.contractibleSpace is a dubious translation:
+lean 3 declaration is
+ forall {E : Type.{u1}} [_inst_1 : AddCommGroup.{u1} E] [_inst_2 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)] [_inst_3 : TopologicalSpace.{u1} E] [_inst_4 : ContinuousAdd.{u1} E _inst_3 (AddZeroClass.toHasAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_1)))))] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_3] {s : Set.{u1} E} {x : E}, (StarConvex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2)))) x s) -> (Set.Nonempty.{u1} E s) -> (ContractibleSpace.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} E) Type.{u1} (Set.hasCoeToSort.{u1} E) s) (Subtype.topologicalSpace.{u1} E (fun (x : E) => Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) x s) _inst_3))
+but is expected to have type
+ forall {E : Type.{u1}} [_inst_1 : AddCommGroup.{u1} E] [_inst_2 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)] [_inst_3 : TopologicalSpace.{u1} E] [_inst_4 : ContinuousAdd.{u1} E _inst_3 (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_1)))))] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_3] {s : Set.{u1} E} {x : E}, (StarConvex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2)))) x s) -> (Set.Nonempty.{u1} E s) -> (ContractibleSpace.{u1} (Set.Elem.{u1} E s) (instTopologicalSpaceSubtype.{u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x s) _inst_3))
+Case conversion may be inaccurate. Consider using '#align star_convex.contractible_space StarConvex.contractibleSpaceₓ'. -/
/-- A non-empty star convex set is a contractible space. -/
protected theorem StarConvex.contractibleSpace (h : StarConvex ℝ x s) (hne : s.Nonempty) :
ContractibleSpace s :=
@@ -42,6 +48,12 @@ protected theorem StarConvex.contractibleSpace (h : StarConvex ℝ x s) (hne : s
simp
#align star_convex.contractible_space StarConvex.contractibleSpace
+/- warning: convex.contractible_space -> Convex.contractibleSpace is a dubious translation:
+lean 3 declaration is
+ forall {E : Type.{u1}} [_inst_1 : AddCommGroup.{u1} E] [_inst_2 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)] [_inst_3 : TopologicalSpace.{u1} E] [_inst_4 : ContinuousAdd.{u1} E _inst_3 (AddZeroClass.toHasAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_1)))))] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_3] {s : Set.{u1} E}, (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2)))) s) -> (Set.Nonempty.{u1} E s) -> (ContractibleSpace.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} E) Type.{u1} (Set.hasCoeToSort.{u1} E) s) (Subtype.topologicalSpace.{u1} E (fun (x : E) => Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) x s) _inst_3))
+but is expected to have type
+ forall {E : Type.{u1}} [_inst_1 : AddCommGroup.{u1} E] [_inst_2 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)] [_inst_3 : TopologicalSpace.{u1} E] [_inst_4 : ContinuousAdd.{u1} E _inst_3 (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_1)))))] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_3] {s : Set.{u1} E}, (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2)))) s) -> (Set.Nonempty.{u1} E s) -> (ContractibleSpace.{u1} (Set.Elem.{u1} E s) (instTopologicalSpaceSubtype.{u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x s) _inst_3))
+Case conversion may be inaccurate. Consider using '#align convex.contractible_space Convex.contractibleSpaceₓ'. -/
/-- A non-empty convex set is a contractible space. -/
protected theorem Convex.contractibleSpace (hs : Convex ℝ s) (hne : s.Nonempty) :
ContractibleSpace s :=
@@ -49,6 +61,12 @@ protected theorem Convex.contractibleSpace (hs : Convex ℝ s) (hne : s.Nonempty
(hs.StarConvex hx).ContractibleSpace hne
#align convex.contractible_space Convex.contractibleSpace
+/- warning: real_topological_vector_space.contractible_space -> RealTopologicalVectorSpace.contractibleSpace is a dubious translation:
+lean 3 declaration is
+ forall {E : Type.{u1}} [_inst_1 : AddCommGroup.{u1} E] [_inst_2 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)] [_inst_3 : TopologicalSpace.{u1} E] [_inst_4 : ContinuousAdd.{u1} E _inst_3 (AddZeroClass.toHasAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_1)))))] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_3], ContractibleSpace.{u1} E _inst_3
+but is expected to have type
+ forall {E : Type.{u1}} [_inst_1 : AddCommGroup.{u1} E] [_inst_2 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)] [_inst_3 : TopologicalSpace.{u1} E] [_inst_4 : ContinuousAdd.{u1} E _inst_3 (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_1)))))] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_3], ContractibleSpace.{u1} E _inst_3
+Case conversion may be inaccurate. Consider using '#align real_topological_vector_space.contractible_space RealTopologicalVectorSpace.contractibleSpaceₓ'. -/
instance (priority := 100) RealTopologicalVectorSpace.contractibleSpace : ContractibleSpace E :=
(Homeomorph.Set.univ E).contractibleSpace_iff.mp <|
convex_univ.ContractibleSpace Set.univ_nonempty
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
mul
-div
cancellation lemmas (#11530)
Lemma names around cancellation of multiplication and division are a mess.
This PR renames a handful of them according to the following table (each big row contains the multiplicative statement, then the three rows contain the GroupWithZero
lemma name, the Group
lemma, the AddGroup
lemma name).
| Statement | New name | Old name | |
@@ -26,7 +26,7 @@ protected theorem StarConvex.contractibleSpace (h : StarConvex ℝ x s) (hne : s
(contractible_iff_id_nullhomotopic s).2
⟨⟨x, h.mem hne⟩,
⟨⟨⟨fun p => ⟨p.1.1 • x + (1 - p.1.1) • (p.2 : E), _⟩, _⟩, fun x => _, fun x => _⟩⟩⟩
- · exact h p.2.2 p.1.2.1 (sub_nonneg.2 p.1.2.2) (add_sub_cancel'_right _ _)
+ · exact h p.2.2 p.1.2.1 (sub_nonneg.2 p.1.2.2) (add_sub_cancel _ _)
· exact
((continuous_subtype_val.fst'.smul continuous_const).add
((continuous_const.sub continuous_subtype_val.fst').smul
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -16,7 +16,7 @@ topological space.
-/
-variable {E : Type _} [AddCommGroup E] [Module ℝ E] [TopologicalSpace E] [ContinuousAdd E]
+variable {E : Type*} [AddCommGroup E] [Module ℝ E] [TopologicalSpace E] [ContinuousAdd E]
[ContinuousSMul ℝ E] {s : Set E} {x : E}
/-- A non-empty star convex set is a contractible space. -/
@@ -2,15 +2,12 @@
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module analysis.convex.contractible
-! leanprover-community/mathlib commit 3339976e2bcae9f1c81e620836d1eb736e3c4700
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Analysis.Convex.Star
import Mathlib.Topology.Homotopy.Contractible
+#align_import analysis.convex.contractible from "leanprover-community/mathlib"@"3339976e2bcae9f1c81e620836d1eb736e3c4700"
+
/-!
# A convex set is contractible
The unported dependencies are
algebra.order.module
init.core
algebra.order.monoid.cancel.defs
algebra.abs
algebra.group_power.lemmas
init.data.list.basic
algebra.order.monoid.cancel.basic
init.data.list.default
topology.subset_properties
init.logic
The following 1 dependencies have changed in mathlib3 since they were ported, which may complicate porting this file