2019-06-27 22:19:00 +03:00
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plusnZ : (n : Nat) -> n + 0 = n
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plusnZ 0 = Refl
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2019-10-26 00:24:25 +03:00
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plusnZ (S k) = rewrite plusnZ k in Refl
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2019-06-27 22:19:00 +03:00
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plusnSm : (n, m : Nat) -> n + (S m) = S (n + m)
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plusnSm Z m = Refl
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plusnSm (S k) m = rewrite plusnSm k m in Refl
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plusCommutes : (n, m : Nat) -> n + m = m + n
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plusCommutes Z m = sym (plusnZ m)
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plusCommutes (S k) m = rewrite plusCommutes k m in sym (plusnSm m k)
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wrongCommutes : (n, m : Nat) -> n + m = m + n
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wrongCommutes Z m = sym (plusnZ m)
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wrongCommutes (S k) m = rewrite plusCommutes m k in ?bar
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wrongCommutes2 : (n, m : Nat) -> n + m = m + n
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wrongCommutes2 Z m = sym (plusnZ m)
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wrongCommutes2 (S k) m = rewrite m in ?bar
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