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Proof step 7 from proof modeqp-03 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
i * j + j0 = i0 * j + j1, j1 < 0, j < j1, j < j0, j < 0, j1 ≤ 0, j0 ≤ 0 ⊦ i = i0 ∧ j0 = j1, j - j1 < 0 ∧ abs(j0) + j < 0

Rule argument

Additional information

Used simplifier rules: 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)% ⊦ 0 - i = ~ i; (s)