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feat(library/standard/decidable): decidable is proof irrelevant

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Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
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Leonardo de Moura 2014-07-22 03:54:28 -07:00
parent 725f370e59
commit 1e595e8027
1 changed files with 12 additions and 0 deletions
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library/standard/decidable.lean
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@ -17,6 +17,18 @@ theorem em (p : Bool) (H : decidable p) : p ∨ ¬p
definition rec [inline] {p : Bool} {C : Type} (H : decidable p) (H1 : p → C) (H2 : ¬p → C) : C definition rec [inline] {p : Bool} {C : Type} (H : decidable p) (H1 : p → C) (H2 : ¬p → C) : C
:= decidable_rec H1 H2 H := decidable_rec H1 H2 H
theorem irrelevant {p : Bool} (d1 d2 : decidable p) : d1 = d2
:= decidable_rec
(assume Hp1 : p, decidable_rec
(assume Hp2 : p, congr2 inl (refl Hp1)) -- using proof irrelevance for Bool
(assume Hnp2 : ¬p, absurd_elim (inl Hp1 = inr Hnp2) Hp1 Hnp2)
d2)
(assume Hnp1 : ¬p, decidable_rec
(assume Hp2 : p, absurd_elim (inr Hnp1 = inl Hp2) Hp2 Hnp1)
(assume Hnp2 : ¬p, congr2 inr (refl Hnp1)) -- using proof irrelevance for Bool
d2)
d1
theorem decidable_true [instance] : decidable true theorem decidable_true [instance] : decidable true
:= inl trivial := inl trivial