13 lines
494 B
Text
13 lines
494 B
Text
inductive Equality {α : Type u} : α → α → Type u
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| refl {a : α} : Equality a a
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open Equality
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@[eliminator]
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def ind {α : Type u} (motive : ∀ (a b : α) (p : Equality a b), Sort v)
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{a : α} (πrefl : motive a a refl) {b : α} (p : Equality a b) : motive a b p :=
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@Equality.casesOn α a (λ b p => motive a a refl → motive a b p) b p
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(λ (ε : motive a a refl) => ε) πrefl
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def symm {α : Type u} {a b : α} (p : Equality a b) : Equality b a :=
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by { induction p; apply refl }
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