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Proof step 23 from proof noeth-modlep (previous step)

0 < j2, j0 < j2, 0 ≤ j0, i0 < i, j ≤ j2, j0 < j, j * i ≤ j * i0 + j0, 0 < j, abs(j - 1) < j2 → abs(j - 1) * i ≤ abs(j - 1) * i0 + j0 ∧ 0 ≤ j0 ∧ j0 < abs(j - 1) → i ≤ i0 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%sub-ls-01: ⊦ i < j - i0 ↔ i + i0 < j; from specification int-abs%zero-gels-04: ⊦ 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%succ-02: ⊦ i < j + 1 ↔ i ≤ j; from specification int-abs%sub-ls: ⊦ i - j < i0 ↔ i < j + i0; from specification int-abs%abs-16: ⊦ 0 < j → abs(j) = j; from specification int-abs%abs-09: ⊦ 0 < i → abs(i - 1) = abs(i) - 1; from specification int-abs