34 lines
828 B
Text
34 lines
828 B
Text
import logic
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namespace setoid
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inductive setoid : Type :=
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mk_setoid: Π (A : Type'), (A → A → Prop) → setoid
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set_option pp.universes true
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check setoid
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definition test : Type.{2} := setoid.{0}
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definition carrier (s : setoid)
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:= setoid.rec (λ a eq, a) s
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definition eqv {s : setoid} : carrier s → carrier s → Prop
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:= setoid.rec (λ a eqv, eqv) s
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infix `≈`:50 := eqv
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coercion carrier
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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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