lean2/tests/lean/run/coe2.lean

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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
attribute carrier [coercion]
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