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feat(library/standard): add iff_mp_right and iff_mp_left

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Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
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Leonardo de Moura 2014-06-30 00:29:42 -07:00
parent ccdb96775f
commit 3650ffdd4f
1 changed files with 6 additions and 0 deletions
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6
library/standard/logic.lean
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@ -98,6 +98,12 @@ theorem iff_elim_left {a b : Bool} (H : a ↔ b) : a → b
theorem iff_elim_right {a b : Bool} (H : a ↔ b) : b → a
:= iff_elim (assume H1 H2, H2) H
theorem iff_mp_left {a b : Bool} (H1 : a ↔ b) (H2 : a) : b
:= (iff_elim_left H1) H2
theorem iff_mp_right {a b : Bool} (H1 : a ↔ b) (H2 : b) : a
:= (iff_elim_right H1) H2
inductive Exists {A : Type} (P : A → Bool) : Bool :=
| exists_intro : ∀ (a : A), P a → Exists P