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Merge master into nightly-testing
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Mathlib.lean

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@@ -5308,6 +5308,7 @@ import Mathlib.RingTheory.LocalRing.ResidueField.Basic
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import Mathlib.RingTheory.LocalRing.ResidueField.Defs
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import Mathlib.RingTheory.LocalRing.ResidueField.Fiber
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import Mathlib.RingTheory.LocalRing.ResidueField.Ideal
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import Mathlib.RingTheory.LocalRing.ResidueField.Instances
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import Mathlib.RingTheory.LocalRing.RingHom.Basic
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import Mathlib.RingTheory.LocalRing.Subring
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import Mathlib.RingTheory.Localization.Algebra

Mathlib/Algebra/Star/NonUnitalSubalgebra.lean

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@@ -602,7 +602,6 @@ variable {R}
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/-- The `NonUnitalStarSubalgebra` obtained from `S : NonUnitalSubalgebra R A` by taking the
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smallest non-unital subalgebra containing both `S` and `star S`. -/
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@[simps!]
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def starClosure (S : NonUnitalSubalgebra R A) : NonUnitalStarSubalgebra R A where
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toNonUnitalSubalgebra := S ⊔ star S
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star_mem' := @fun a (ha : a ∈ S ⊔ star S) => show star a ∈ S ⊔ star S by
@@ -611,9 +610,11 @@ def starClosure (S : NonUnitalSubalgebra R A) : NonUnitalStarSubalgebra R A wher
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simp only [Set.sup_eq_union, star_adjoin_comm, Set.union_star, coe_star, star_star,
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Set.union_comm]
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@[simp]
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theorem coe_starClosure (S : NonUnitalSubalgebra R A) :
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(S.starClosure : Set A) = (S ⊔ star S : NonUnitalSubalgebra R A) := rfl
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@[simp]
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theorem mem_starClosure (S : NonUnitalSubalgebra R A) {x : A} :
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x ∈ S.starClosure ↔ x ∈ S ⊔ star S := Iff.rfl
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Mathlib/Algebra/Star/Subalgebra.lean

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@@ -368,17 +368,18 @@ theorem star_adjoin_comm (s : Set A) : star (Algebra.adjoin R s) = Algebra.adjoi
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/-- The `StarSubalgebra` obtained from `S : Subalgebra R A` by taking the smallest subalgebra
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containing both `S` and `star S`. -/
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@[simps!]
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def starClosure (S : Subalgebra R A) : StarSubalgebra R A where
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toSubalgebra := S ⊔ star S
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star_mem' := fun {a} ha => by
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simp only [Subalgebra.mem_carrier, ← (@Algebra.gi R A _ _ _).l_sup_u _ _] at *
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rw [← mem_star_iff _ a, star_adjoin_comm, sup_comm]
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simpa using ha
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@[simp]
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theorem coe_starClosure (S : Subalgebra R A) :
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(S.starClosure : Set A) = (S ⊔ star S : Subalgebra R A) := rfl
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@[simp]
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theorem mem_starClosure (S : Subalgebra R A) {x : A} :
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x ∈ S.starClosure ↔ x ∈ S ⊔ star S := Iff.rfl
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Mathlib/Analysis/Convex/Cone/Closure.lean

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@@ -17,7 +17,7 @@ defining maps between proper cones. The current API is basic and should be exten
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namespace ConvexCone
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variable {𝕜 : Type*} [Semiring 𝕜] [PartialOrder 𝕜] [IsOrderedRing 𝕜]
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variable {𝕜 : Type*} [Semiring 𝕜] [PartialOrder 𝕜]
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variable {E : Type*} [AddCommMonoid E] [TopologicalSpace E] [ContinuousAdd E] [SMul 𝕜 E]
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[ContinuousConstSMul 𝕜 E]
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@@ -53,7 +53,7 @@ variable {E : Type*} [AddCommMonoid E] [TopologicalSpace E] [ContinuousAdd E] [M
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[ContinuousConstSMul 𝕜 E]
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lemma toConvexCone_closure_pointed (K : PointedCone 𝕜 E) : (K : ConvexCone 𝕜 E).closure.Pointed :=
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subset_closure <| PointedCone.toConvexCone_pointed _
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subset_closure <| PointedCone.pointed_toConvexCone _
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/-- The closure of a pointed cone inside a topological space as a pointed cone. This
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construction is mainly used for defining maps between proper cones. -/

Mathlib/Analysis/Convex/Cone/InnerDual.lean

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@@ -266,7 +266,7 @@ theorem hyperplane_separation (K : ProperCone ℝ H) {f : H →L[ℝ] F} {b : F}
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intro h
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contrapose! h
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-- as `b ∉ K.map f`, there is a hyperplane `y` separating `b` from `K.map f`
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let C := PointedCone.toConvexCone (𝕜 := ℝ) (E := F) (K.map f)
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let C := PointedCone.toConvexCone (R := ℝ) (E := F) (K.map f)
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obtain ⟨y, hxy, hyb⟩ :=
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@ConvexCone.hyperplane_separation_of_nonempty_of_isClosed_of_notMem
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_ _ _ _ C (K.map f).nonempty (K.map f).isClosed b h

Mathlib/CategoryTheory/Monoidal/Action/Basic.lean

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@@ -100,7 +100,6 @@ scoped notation "λₗ["J"]" => MonoidalLeftActionStruct.actionUnitIso (C := J)
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end MonoidalLeftAction
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open scoped MonoidalLeftAction in
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/-- A `MonoidalLeftAction C D` is is the data of:
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- For every object `c : C` and `d : D`, an object `c ⊙ₗ d` of `D`.
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- For every morphism `f : (c : C) ⟶ c'` and every `d : D`, a morphism

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