13 lines
345 B
Text
13 lines
345 B
Text
variable {A : Type}
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structure has_refl (R : A → A → Prop) : Prop :=
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(refl : ∀ a, R a a)
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structure is_equiv (R : A → A → Prop) extends has_refl R : Prop :=
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(symm : ∀ a b, R a b → R b a)
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(trans : ∀ a b c, R a b → R b c → R a c)
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#check @is_equiv.refl
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#check @is_equiv.symm
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#check @is_equiv.trans
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#check @is_equiv.to_has_refl
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