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Proof step 25 from proof mod-rec-neg (previous step)

j0 % j < j + j0, j0 % j < 0, j0 < j, j0 < 0, i0 < j + j0, i0 < j, 0 < j, 0 < j + j0, i0 < 0, (i0 + 1) * j + j0 < 0 ⊦ j0 = j0 % j

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: mod-zero-05 seq: ⊦ abs(i) < j → i % j = i subst: [j, i] → [j, j0] flags: rewrite

Additional information

Used simplifier rules: abs-08: ⊦ i < 0 → abs(i) = ~ i; from specification int-abs%neg-13: ⊦ ~ i < j ↔ 0 < j + i; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs Used terms: j, j0