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Proof step 30 from proof exdivmod (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
i + i0 * j + j0 = 0, 0 ≤ j0, 0 ≤ i0, j0 < j, i ≤ 0, i < 0, 0 < j ⊦ i0 * j + i = 0, j - j0 < j

Rule argument

Additional information

Used simplifier rules: minus-left: ⊦ ~ i * j = ~(i * j);%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%negeq: ⊦ ~ i = j ↔ i + j = 0; from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-zero: ⊦ i + 0 = i; from specification int-basic2