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Proof step 10 from proof modlep-04 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
abs(j1) < j, i0 < i, j * i0 < j0 + j * i + abs(j1), j1 < j + j0, j0 < 0, 0 < j + j0, j * i + j0 ≤ j * i0 + j1, j1 ≤ 0 ⊦

Rule argument

Additional information

Used simplifier rules: forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs% ⊦ i - j < i0 ↔ i < j + i0; (s)%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ i + ~ j = i - j; (s)% ⊦ ~ i < j ↔ 0 < j + i; (s)% ⊦ 0 - i = ~ i; (s)% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; (s)