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18 lines
518 B
Idris
18 lines
518 B
Idris
plus_commutes_Z : (m : Nat) -> m = plus m Z
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plus_commutes_Z Z = Refl
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plus_commutes_Z (S k)
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= let rec = plus_commutes_Z k in
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rewrite sym rec in Refl
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plus_commutes_S : (k : Nat) -> (m : Nat) -> S (plus m k) = plus m (S k)
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plus_commutes_S k Z = Refl
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plus_commutes_S k (S j)
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= rewrite plus_commutes_S k j in Refl
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total
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plus_commutes : (n : Nat) -> (m : Nat) -> n + m = m + n
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plus_commutes Z m = plus_commutes_Z m
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plus_commutes (S k) m
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= rewrite plus_commutes k m in
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plus_commutes_S k m
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