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24 lines
No EOL
838 B
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-- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
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-- Released under Apache 2.0 license as described in the file LICENSE.
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-- Author: Leonardo de Moura
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import logic function
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using function
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-- Function extensionality
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axiom funext : ∀ {A : Type} {B : A → Type} {f g : Π x, B x} (H : ∀ x, f x = g x), f = g
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namespace function
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section
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parameters {A : Type} {B : Type} {C : Type} {D : Type}
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theorem compose_assoc (f : C → D) (g : B → C) (h : A → B) : (f ∘ g) ∘ h = f ∘ (g ∘ h) :=
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funext (take x, refl _)
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theorem compose_id_left (f : A → B) : id ∘ f = f :=
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funext (take x, refl _)
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theorem compose_id_right (f : A → B) : f ∘ id = f :=
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funext (take x, refl _)
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theorem compose_const_right (f : B → C) (b : B) : f ∘ (const A b) = const A (f b) :=
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funext (take x, refl _)
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end end |