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Proof step 4 from proof modeqp-03 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

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;% ⊦ 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)