Another example for eHoare #845
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Jan 10, 2026
| require import StdOrder. | ||
| (*---*) import RealOrder. | ||
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| lemma mul0z (x : int) : 0 * x = 0. |
| lemma mul0z (x : int) : 0 * x = 0. | ||
| proof. by auto. qed. | ||
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| lemma neg0: -0 = 0. |
| lemma neg0: -0 = 0. | ||
| proof. by auto. qed. | ||
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| lemma xle_rle: |
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Surprised if it does not exist. If not, move it to the standard library.
| by rewrite !to_pos_pos //; exact (ler_trans x). | ||
| qed. | ||
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| lemma Ep_dbiased (p : real) (f : bool -> xreal) : |
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Move it to the standard library. Use the link to the E to reuse the proof.
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Another example for eHoare (done with @mzini). This example considers a nested loop which uniformly samples a boolean matrix of size$n \times m$ , and proves that the probably of sampling any boolean matrix of size $n \times m$ is no more than $2 ^ {- n \times m}$ .
My original purpose for this example was to figure out a game hopping in a big proof, but it turned out that this game hopping is not needed. But I think this is a good example for demonstrating how to do proof in eHoare.