diff --git a/library/init/funext.lean b/library/init/funext.lean index acef03bf4..7a05a4883 100644 --- a/library/init/funext.lean +++ b/library/init/funext.lean @@ -2,21 +2,21 @@ Copyright (c) 2015 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. +Module: init.funext Author: Jeremy Avigad -function extensionality from quotients +Function extensionality follows from quotients. -/ prelude import init.quot init.logic -/- function extensionality follows from quotients -/ section open quot variables {A : Type} {B : A → Type} private definition fun_eqv (f₁ f₂ : Πx : A, B x) : Prop := ∀x, f₁ x = f₂ x - infix `~` := fun_eqv -- this is "~" + infix `~` := fun_eqv private theorem fun_eqv.refl (f : Πx : A, B x) : f ~ f := take x, rfl diff --git a/library/init/quot.lean b/library/init/quot.lean index 4a1e465a7..83cd77a2d 100644 --- a/library/init/quot.lean +++ b/library/init/quot.lean @@ -2,9 +2,10 @@ Copyright (c) 2015 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. +Module: init.quot Author: Leonardo de Moura -Quotient types +Quotient types. -/ prelude import init.sigma init.setoid init.logic