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Proof step 7 from proof modlep-04 (previous step)

j * i0 + abs(j0) < j * i + abs(j1), i0 < i, abs(j0) < j, abs(j1) < j, j0 ≤ 0, j1 ≤ 0, j * i + j0 ≤ j * i0 + j1 ⊦ j0 < 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
j * i0 < j * i + abs(j1), i0 < i, abs(j1) < j, 0 < j, j1 < j, j1 ≤ 0, j * i ≤ j * i0 + j1 ⊦

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) 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% ⊦ i + 0 = i; (s)% ⊦ i ≤ j → (j ≤ i ↔ i = j); (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ ¬ j < 0 → abs(j) = j; (s)