fix(tests/lean): to reflect changes in the standard library
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5 changed files with 3 additions and 48 deletions
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VISIT calc_assistant.lean
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SYNC 13
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import logic algebra.category.basic
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open eq eq.ops category functor natural_transformation
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variables {obC obD : Type} {C : category obC} {D : category obD} {F G H : C ⇒ D}
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protected definition compose2 (η : G ⟹ H) (θ : F ⟹ G) : F ⟹ H :=
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natural_transformation.mk
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(λ a, η a ∘ θ a)
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(λ a b f, calc
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H f ∘ (η a ∘ θ a) = (H f ∘ η a) ∘ θ a : assoc
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... = (η b ∘ G f) ∘ θ a : naturality η f
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... = η b ∘ (G f ∘ θ a) :
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assoc
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... = η b ∘ (θ b ∘ F f) : naturality θ f
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... = (η b ∘ θ b) ∘ F f : assoc)
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WAIT
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INFO 11
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-- BEGINWAIT
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-- ENDWAIT
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-- BEGININFO
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-- TYPE|11|28
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η b ∘ G f ∘ θ a = (η b ∘ G f) ∘ θ a
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-- ACK
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-- IDENTIFIER|11|28
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category.assoc
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-- ACK
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-- ENDINFO
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funext : ∀ {A : Type} {B : A → Type} {f g : Π (x : A), B x}, (∀ (x : A), f x = g x) → f = g
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funext : ∀ {A : Type} {B : A → Type} {f g : Π (a : A), B a}, (∀ (a : A), f a = g a) → f = g
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strong_indefinite_description : Π {A : Type} (P : A → Prop), nonempty A → { (x : A), (∃ (x : A), P x) → P x }
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strong_indefinite_description : Π {A : Type} (P : A → Prop), nonempty A → { (x : A), (∃ (x : A), P x) → P x }
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import logic algebra.category.basic
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open eq eq.ops category functor natural_transformation
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variables {obC obD : Type} {C : category obC} {D : category obD} {F G H : C ⇒ D}
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protected definition compose2 (η : G ⟹ H) (θ : F ⟹ G) : F ⟹ H :=
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natural_transformation.mk
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(λ a, η a ∘ θ a)
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(λ a b f, calc
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H f ∘ (η a ∘ θ a) = (H f ∘ η a) ∘ θ a : assoc
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... = (η b ∘ G f) ∘ θ a : naturality η f
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... = η b ∘ (G f ∘ θ a) : assoc
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... = η b ∘ (θ b ∘ F f) : naturality θ f
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... = (η b ∘ θ b) ∘ F f : assoc)
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theorem tst (a b c : num) (H₁ : ∀ x, b = x) (H₂ : c = b) : a = c :=
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calc a = b : H₁
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... = c : H₂
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import data.num logic data.prod data.nat data.int algebra.category.basic
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import data.num logic data.prod data.nat data.int algebra.category.basic
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open num prod int nat category functor
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open num prod int nat category
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print instances inhabited
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print instances inhabited
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print raw 3+2
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print raw 3+2
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print options
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print options
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print coercions functor
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print coercions Category
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print "-----------"
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print "-----------"
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print coercions
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print coercions
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print "-----------"
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print "-----------"
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