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Proof step 4 from proof modeqp-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: ⊦ ~ i < j ↔ 0 < j + i; (s)% ⊦ i + 0 = i; (s)% ⊦ i ≤ ~ j ↔ i + j ≤ 0; (s)% ⊦ i + (j - i0) = i + j - i0; (s)% ⊦ i - j = i0 ↔ i = i0 + j; (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)