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Proof step 2 from proof modlsp-06 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
j < j1, j * i + j0 < j * i0 + j1, j < 0, i < i0, abs(j0) + j < 0, j1 ≤ 0 ⊦

Rule argument

Additional information

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