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Proof step 24 from proof mod-rec-neg (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: mod-less-01: ⊦ 0 < j → i % j < j; from specification int-div%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%transitivity: ⊦ i < i0 ∧ i0 < i1 → i < i1; (forward) from specification oelem[intlista]%zero-gels-03: ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%mone-05: ⊦ i ≤ ~1 ↔ i < 0; from specification int-abs%numle-03: ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j; from specification int-abs