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refactor(library/logic/if): mark basic theorem transparent

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Leonardo de Moura 2014-11-21 20:23:46 -08:00
parent acf1c501ad
commit 7c54dbce10
1 changed files with 5 additions and 5 deletions
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library/logic/if.lean
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@ -12,28 +12,28 @@ decidable.rec_on H (assume Hc, t) (assume Hnc, e)
notation `if` c `then` t:45 `else` e:45 := ite c t e
theorem if_pos {c : Prop} [H : decidable c] (Hc : c) {A : Type} {t e : A} : (if c then t else e) = t :=
definition if_pos {c : Prop} [H : decidable c] (Hc : c) {A : Type} {t e : A} : (if c then t else e) = t :=
decidable.rec
(assume Hc : c, eq.refl (@ite c (inl Hc) A t e))
(assume Hnc : ¬c, absurd Hc Hnc)
H
theorem if_neg {c : Prop} [H : decidable c] (Hnc : ¬c) {A : Type} {t e : A} : (if c then t else e) = e :=
definition if_neg {c : Prop} [H : decidable c] (Hnc : ¬c) {A : Type} {t e : A} : (if c then t else e) = e :=
decidable.rec
(assume Hc : c, absurd Hc Hnc)
(assume Hnc : ¬c, eq.refl (@ite c (inr Hnc) A t e))
H
theorem if_t_t (c : Prop) [H : decidable c] {A : Type} (t : A) : (if c then t else t) = t :=
definition if_t_t (c : Prop) [H : decidable c] {A : Type} (t : A) : (if c then t else t) = t :=
decidable.rec
(assume Hc : c, eq.refl (@ite c (inl Hc) A t t))
(assume Hnc : ¬c, eq.refl (@ite c (inr Hnc) A t t))
H
theorem if_true {A : Type} (t e : A) : (if true then t else e) = t :=
definition if_true {A : Type} (t e : A) : (if true then t else e) = t :=
if_pos trivial
theorem if_false {A : Type} (t e : A) : (if false then t else e) = e :=
definition if_false {A : Type} (t e : A) : (if false then t else e) = e :=
if_neg not_false_trivial
theorem if_cond_congr {c₁ c₂ : Prop} [H₁ : decidable c₁] [H₂ : decidable c₂] (Heq : c₁ ↔ c₂) {A : Type} (t e : A)