20 lines
477 B
Text
20 lines
477 B
Text
import logic
|
|
|
|
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 `≈` := 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 setoid
|