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Proof step 4 from proof modlep-04 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
abs(j1) < j, abs(j0) < j, i0 < i, j * i0 + abs(j0) < j * i + abs(j1), j * i + j0 ≤ j * i0 + j1, j1 ≤ 0, j0 ≤ 0 ⊦

Rule argument

Additional information

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