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feat(hott,library): auxiliary theorems for simplifier

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Leonardo de Moura 2015-05-26 16:08:01 -07:00
parent 85409a59d3
commit 00232e70d6
2 changed files with 12 additions and 2 deletions
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5
hott/init/logic.hlean
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@ -338,6 +338,11 @@ definition if_congr {c₁ c₂ : Type} [H₁ : decidable c₁] {A : Type} {t₁
have H2 [visible] : decidable c₂, from (decidable.decidable_iff_equiv H₁ Hc),
if_congr_aux Hc Ht He
theorem implies_of_if_pos {c t e : Type} [H : decidable c] (h : if c then t else e) : c → t :=
assume Hc, eq.rec_on (if_pos Hc) h
theorem implies_of_if_neg {c t e : Type} [H : decidable c] (h : if c then t else e) : ¬c → e :=
assume Hnc, eq.rec_on (if_neg Hnc) h
-- We use "dependent" if-then-else to be able to communicate the if-then-else condition
-- to the branches

9
library/init/logic.lean
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@ -117,8 +117,7 @@ namespace ne
end ne
section
open eq.ops
variables {A : Type} {a b c : A}
variables {A : Type} {a : A}
theorem false.of_ne : a ≠ a → false :=
assume H, H rfl
@ -501,6 +500,12 @@ decidable.rec
(λ Hnc : ¬c, eq.refl (@ite c (decidable.inr Hnc) A t t))
H
theorem implies_of_if_pos {c t e : Prop} [H : decidable c] (h : if c then t else e) : c → t :=
assume Hc, eq.rec_on (if_pos Hc) h
theorem implies_of_if_neg {c t e : Prop} [H : decidable c] (h : if c then t else e) : ¬c → e :=
assume Hnc, eq.rec_on (if_neg Hnc) h
-- We use "dependent" if-then-else to be able to communicate the if-then-else condition
-- to the branches
definition dite (c : Prop) [H : decidable c] {A : Type} (t : c → A) (e : ¬ c → A) : A :=