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Proof step 3 from proof modlep-04 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
j * i + j0 ≤ j * i0 + j1, abs(j0) < j, abs(j1) < j, i0 < i, j * i0 + abs(j0) < j * i + abs(j1), j0 ≤ 0, j1 ≤ 0 ⊦

Rule argument

Additional information

Used simplifier rules: forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%abs-01: ⊦ abs(abs(i)) = abs(i); from specification int-abs%abs-03: ⊦ 0 ≤ abs(i); from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs