23 lines
553 B
Text
23 lines
553 B
Text
open nat
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inductive fin : nat → Type :=
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| fz : Π n, fin (succ n)
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| fs : Π {n}, fin n → fin (succ n)
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namespace fin
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definition z_cases_on2 (C : fin zero → Type) (p : fin zero) : C p :=
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by cases p
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definition nz_cases_on2 {C : Π n, fin (succ n) → Type}
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(H₁ : Π n, C n (fz n))
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(H₂ : Π n (f : fin n), C n (fs f))
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{n : nat}
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(f : fin (succ n)) : C n f :=
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begin
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cases f,
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apply (H₁ n),
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apply (H₂ n a)
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end
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end fin
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