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15 lines
488 B
Idris
15 lines
488 B
Idris
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plus2 : Nat -> Nat
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plus2 = S . S
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okplus2Injective : (x, y : Nat) -> Equal (plus2 x) (plus2 y) -> Equal x y
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okplus2Injective Z Z Refl = Refl
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okplus2Injective (S n) (S n) Refl = Refl
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okplus2Injective Z (S _) _ impossible
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okplus2Injective (S _) Z _ impossible
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badplus2Injective : (x, y : Nat) -> Equal (plus2 x) (plus2 y) -> Equal x y
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badplus2Injective Z Z Refl = Refl
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badplus2Injective Z (S _) _ impossible
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badplus2Injective (S _) Z _ impossible
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badplus2Injective (S n) (S n) Refl = Refl
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