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Add not LTE implies GT, and LTE implies maximum.#4428
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LeifW wants to merge 2 commits intoidris-lang:masterfrom
Open
Add not LTE implies GT, and LTE implies maximum.#4428LeifW wants to merge 2 commits intoidris-lang:masterfrom
LeifW wants to merge 2 commits intoidris-lang:masterfrom
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ahmadsalim
reviewed
Apr 27, 2018
| isLTE (S k) (S j) with (isLTE k j) | ||
| isLTE (S k) (S j) | (Yes prf) = Yes (LTESucc prf) | ||
| isLTE (S k) (S j) | (No contra) = No (contra . fromLteSucc) | ||
| isLTE (S k) (S j) = case isLTE k j of |
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Is there any reason for the change here? 😄
ahmadsalim
reviewed
Apr 27, 2018
| sucMinR Z = Refl | ||
| sucMinR (S l) = cong (sucMinR l) | ||
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| ||| If one number is biggre than another, you know what the maximum is. |
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There is a small typo biggre -> bigger
ahmadsalim
reviewed
Apr 27, 2018
| sucMinR (S l) = cong (sucMinR l) | ||
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| ||| If one number is biggre than another, you know what the maximum is. | ||
| total lteImpliesMax : i `LTE` j -> maximum i j = j |
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Maybe this should be added to contrib instead of prelude?
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On the existing
notLTImpliesGTE- wasn't sure if there was a way I could use it (besides cribbing from its implementation), so I just implementednotLTEImpliesGT, so I could apply it to the disproof returned byisLTE, as in:As for
lteImpliesMax, I figure knowing which number is greater should enable you to say something about the maximum, or at least they should be related, somehow. I needed it for something I was working on.