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30 lines
678 B
Idris
30 lines
678 B
Idris
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fiveIsFive : 5 = 5
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fiveIsFive = Refl
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twoPlusTwo : 2 + 2 = 4
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twoPlusTwo = Refl
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-- twoPlusTwoBad : 2 + 2 = 5
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-- twoPlusTwoBad = Refl
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disjoint : (n : Nat) -> Z = S n -> Void
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disjoint n prf = replace {p = disjointTy} prf ()
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where
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disjointTy : Nat -> Type
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disjointTy Z = ()
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disjointTy (S k) = Void
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plusReduces : (n:Nat) -> plus Z n = n
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plusReduces n = Refl
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plusReducesR : (n:Nat) -> plus n Z = n
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plusReducesR n = Refl
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plusReducesZ : (n:Nat) -> n = plus n Z
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plusReducesZ Z = Refl
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plusReducesZ (S k) = cong S (plusReducesZ k)
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plusReducesS : (n:Nat) -> (m:Nat) -> S (plus n m) = plus n (S m)
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plusReducesS Z m = Refl
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plusReducesS (S k) m = cong S (plusReducesS k m)
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