26 lines
652 B
Text
26 lines
652 B
Text
import logic
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namespace setoid
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structure setoid : Type :=
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(carrier : Type) (eqv : carrier → carrier → Prop)
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infix `≈` := setoid.eqv _
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attribute setoid.carrier [coercion]
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check setoid
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definition test : Type.{1} := setoid.{0}
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inductive morphism (s1 s2 : setoid) : Type :=
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mk : Π (f : s1 → s2), (∀ x y, x ≈ y → f x ≈ f y) → morphism s1 s2
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check morphism.mk
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check λ (s1 s2 : setoid), s1
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check λ (s1 s2 : Type), s1
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inductive morphism2 (s1 : setoid) (s2 : setoid) : Type :=
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mk : Π (f : s1 → s2), (∀ x y, x ≈ y → f x ≈ f y) → morphism2 s1 s2
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check morphism2
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check morphism2.mk
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end setoid
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