lean2/tests/lean/run/coe2.lean
Leonardo de Moura 5eaf04518b refactor(*): rename Bool to Prop
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-07-22 09:43:18 -07:00

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import standard
namespace setoid
inductive setoid : Type :=
| mk_setoid: Π (A : Type), (A → A → Prop) → setoid
definition carrier (s : setoid)
:= setoid_rec (λ a eq, a) s
definition eqv {s : setoid} : carrier s → carrier s → Prop
:= setoid_rec (λ a eqv, eqv) s
infix `≈`:50 := eqv
coercion carrier
inductive morphism (s1 s2 : setoid) : Type :=
| mk_morphism : Π (f : s1 → s2), (∀ x y, x ≈ y → f x ≈ f y) → morphism s1 s2
end