19 lines
706 B
Text
19 lines
706 B
Text
/-
|
|
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
|
|
Released under Apache 2.0 license as described in the file LICENSE.
|
|
Author: Leonardo de Moura
|
|
|
|
Additional congruence lemmas.
|
|
-/
|
|
prelude
|
|
import init.quot
|
|
universe variables u v
|
|
|
|
lemma forall_congr_eq {A : Type u} {p q : A → Prop} (h : ∀ a, p a = q a) : (∀ a, p a) = ∀ a, q a :=
|
|
propext (forall_congr (λ a, (h a)^.to_iff))
|
|
|
|
lemma imp_congr_eq {a b c d : Prop} (h₁ : a = c) (h₂ : b = d) : (a → b) = (c → d) :=
|
|
propext (imp_congr h₁^.to_iff h₂^.to_iff)
|
|
|
|
lemma imp_congr_ctx_eq {a b c d : Prop} (h₁ : a = c) (h₂ : c → (b = d)) : (a → b) = (c → d) :=
|
|
propext (imp_congr_ctx h₁^.to_iff (λ hc, (h₂ hc)^.to_iff))
|