fix(tests/lean): to reflect changes in the standard library

This commit is contained in:
Leonardo de Moura 2014-11-28 23:03:37 -08:00
parent ae0daf9639
commit 7000365a04
3 changed files with 3 additions and 16 deletions

View file

@ -20,7 +20,7 @@ context sec_cat
parameters {ob : Type} {mor : ob → ob → Type} {Cat : category ob mor}
definition compose := rec (λ comp id assoc idr idl, comp) Cat
definition id := rec (λ comp id assoc idr idl, id) Cat
infixr `∘`:60 := compose
infixr := compose
inductive is_section {A B : ob} (f : mor A B) : Type :=
mk : ∀g, g ∘ f = id → is_section f
end sec_cat

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@ -20,6 +20,6 @@ section sec_cat
variables {ob : Type} {mor : ob → ob → Type} {Cat : category ob mor}
definition compose := rec (λ comp id assoc idr idl, comp) Cat
definition id := rec (λ comp id assoc idr idl, id) Cat
infixr `∘`:60 := compose
infixr := compose
end sec_cat
end category

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@ -2,24 +2,11 @@ import logic algebra.relation
open relation
namespace is_equivalence
inductive cls {T : Type} (R : T → T → Type) : Prop :=
inductive cls {T : Type} (R : T → T → Prop) : Prop :=
mk : is_reflexive R → is_symmetric R → is_transitive R → cls R
theorem is_reflexive {T : Type} {R : T → T → Type} {C : cls R} : is_reflexive R :=
cls.rec (λx y z, x) C
theorem is_symmetric {T : Type} {R : T → T → Type} {C : cls R} : is_symmetric R :=
cls.rec (λx y z, y) C
theorem is_transitive {T : Type} {R : T → T → Type} {C : cls R} : is_transitive R :=
cls.rec (λx y z, z) C
end is_equivalence
instance is_equivalence.is_reflexive
instance is_equivalence.is_symmetric
instance is_equivalence.is_transitive
theorem and_inhabited_left {a : Prop} (b : Prop) (Ha : a) : a ∧ b ↔ b :=
iff.intro (take Hab, and.elim_right Hab) (take Hb, and.intro Ha Hb)