lean2/tests/lean/run/impbug3.lean

prelude
-- category

definition Prop := Type.{0}
constant eq {A : Type} : A → A → Prop
infix `=`:50 := eq

constant ob  : Type.{1}
constant mor : ob → ob → Type.{1}

inductive category : Type :=
mk : Π (id : Π (A : ob), mor A A),
     (Π (A B : ob) (f : mor A A), id A = f) → category

definition id (Cat : category) := category.rec (λ id idl, id) Cat
constant Cat : category

reducible id
theorem id_left (A : ob) (f : mor A A) : @eq (mor A A) (id Cat A) f :=
@category.rec (λ (C : category), @eq (mor A A) (id C A) f)
  (λ (id  : Π (T : ob), mor T T)
     (idl : Π (T : ob), _),
     idl A A f)
  Cat
fix(tests/lean): adjust tests to modifications to standard library 2014-12-01 05:16:01 +00:00			`prelude`
feat(library/unifier): consider whnf case-split on flex-rigid constraints whenever the rhs contains a local constant that is not in the lhs 2014-09-09 16:25:35 +00:00			`-- category`

feat(frontends/lean): definitions are opaque by default 2014-09-17 21:39:05 +00:00			`definition Prop := Type.{0}`
refactor(frontends/lean): constant/axiom are top-level commands, parameter/variable/hypothesis/conjecture are section/context-level commands Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-10-02 23:20:52 +00:00			`constant eq {A : Type} : A → A → Prop`
feat(library/unifier): consider whnf case-split on flex-rigid constraints whenever the rhs contains a local constant that is not in the lhs 2014-09-09 16:25:35 +00:00			infix `=`:50 := eq

refactor(frontends/lean): constant/axiom are top-level commands, parameter/variable/hypothesis/conjecture are section/context-level commands Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-10-02 23:20:52 +00:00			`constant ob : Type.{1}`
			`constant mor : ob → ob → Type.{1}`
feat(library/unifier): consider whnf case-split on flex-rigid constraints whenever the rhs contains a local constant that is not in the lhs 2014-09-09 16:25:35 +00:00
			`inductive category : Type :=`
			`mk : Π (id : Π (A : ob), mor A A),`
			`(Π (A B : ob) (f : mor A A), id A = f) → category`

feat(frontends/lean): definitions are opaque by default 2014-09-17 21:39:05 +00:00			`definition id (Cat : category) := category.rec (λ id idl, id) Cat`
refactor(frontends/lean): constant/axiom are top-level commands, parameter/variable/hypothesis/conjecture are section/context-level commands Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-10-02 23:20:52 +00:00			`constant Cat : category`
feat(library/unifier): consider whnf case-split on flex-rigid constraints whenever the rhs contains a local constant that is not in the lhs 2014-09-09 16:25:35 +00:00
refactor(library/reducible): simplify reducible/irreducible semantics 2015-01-09 02:47:44 +00:00			`reducible id`
feat(library/unifier): consider whnf case-split on flex-rigid constraints whenever the rhs contains a local constant that is not in the lhs 2014-09-09 16:25:35 +00:00			`theorem id_left (A : ob) (f : mor A A) : @eq (mor A A) (id Cat A) f :=`
			`@category.rec (λ (C : category), @eq (mor A A) (id C A) f)`
			`(λ (id : Π (T : ob), mor T T)`
			`(idl : Π (T : ob), _),`
			`idl A A f)`
			`Cat`