Created
July 31, 2013 20:10
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plus commutes
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| plus_comm : (n : Nat) -> (m : Nat) -> (n + m = m + n) | |
| -- Base case | |
| (O + m = m + O) <== plus_comm = | |
| rewrite ((m + O = m) <== plusZeroRightNeutral) ==> | |
| (O + m = m) in refl | |
| -- Step case | |
| (S k + m = m + S k) <== plus_comm = | |
| rewrite ((k + m = m + k) <== plus_comm) in | |
| rewrite ((S (m + k) = m + S k) <== plusSuccRightSucc) in | |
| refl | |
| -- QED |
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This is linked as a syntax example from release notes (http://www.idris-lang.org/idris-0-9-9-released/), but has bitrotted. A up-to-date example version of this can be found in the tests: https://github.com/idris-lang/Idris-dev/blob/master/test/proof001/test029.idr