refactor(library/algebra): fix theorem names
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4 changed files with 57 additions and 57 deletions
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@ -276,7 +276,7 @@ end complete_lattice
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section
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section
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open eq.ops complete_lattice
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open eq.ops complete_lattice
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definition complete_lattice_fun [instance] {A B : Type} [complete_lattice B] :
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definition complete_lattice_fun [instance] (A B : Type) [complete_lattice B] :
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complete_lattice (A → B) :=
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complete_lattice (A → B) :=
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⦃ complete_lattice, lattice_fun,
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⦃ complete_lattice, lattice_fun,
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Inf := λS x, Inf ((λf, f x) ' S),
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Inf := λS x, Inf ((λf, f x) ' S),
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@ -308,7 +308,7 @@ definition complete_lattice_Prop [instance] : complete_lattice Prop :=
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H _ Ht true.intro
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H _ Ht true.intro
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⦄
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⦄
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lemma sInter_eq_fun_Inf {A : Type} (S : set (set A)) : ⋂₀ S = @Inf (A → Prop) _ S :=
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lemma sInter_eq_Inf_fun {A : Type} (S : set (set A)) : ⋂₀ S = @Inf (A → Prop) _ S :=
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funext (take x,
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funext (take x,
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calc
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calc
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(⋂₀ S) x = ∀₀ P ∈ S, P x : rfl
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(⋂₀ S) x = ∀₀ P ∈ S, P x : rfl
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@ -322,19 +322,19 @@ funext (take x,
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end
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end
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... = @Inf (A → Prop) _ S x : rfl)
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... = @Inf (A → Prop) _ S x : rfl)
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lemma sUnion_eq_fun_Sup {A : Type} (S : set (set A)) : ⋃₀ S = @Sup (A → Prop) _ S :=
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lemma sUnion_eq_Sup_fun {A : Type} (S : set (set A)) : ⋃₀ S = @Sup (A → Prop) _ S :=
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funext (take x,
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funext (take x,
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calc
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calc
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(⋃₀ S) x = ∃₀ P ∈ S, P x : rfl
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(⋃₀ S) x = ∃₀ P ∈ S, P x : rfl
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... = (∃₀ P ∈ S, P x = true) :
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... = (∃₀ P ∈ S, P x = true) :
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begin |