Add not LTE implies GT, and LTE implies maximum. #4428
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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
| @@ -840,3 +846,9 @@ sucMinL (S l) = cong (sucMinL l) | |||
| total sucMinR : (l : Nat) -> minimum l (S l) = l | |||
| 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
| @@ -840,3 +846,9 @@ sucMinL (S l) = cong (sucMinL l) | |||
| total sucMinR : (l : Nat) -> minimum l (S l) = l | |||
| 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. | |||
| 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.