lean2/tests/lean/run/coe4.lean

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import logic
namespace setoid
inductive setoid : Type :=
mk_setoid: Π (A : Type'), (A → A → Prop) → setoid
set_option pp.universes true
check setoid
definition test : Type.{2} := setoid.{0}
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 : Π (f : s1 → s2), (∀ x y, x ≈ y → f x ≈ f y) → morphism s1 s2
check morphism.mk
check λ (s1 s2 : setoid), s1
check λ (s1 s2 : Type), s1
inductive morphism2 (s1 : setoid) (s2 : setoid) : Type :=
mk : Π (f : s1 → s2), (∀ x y, x ≈ y → f x ≈ f y) → morphism2 s1 s2
check morphism2
check morphism2.mk
end setoid