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Proof step 3 from proof modeqp-03 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
i * j + j0 = i0 * j + j1, j < j0, j < j1, j0 ≤ 0, j1 ≤ 0, j < 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;%forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%neg-07: ⊦ i < ~ j ↔ i + j < 0; from specification int-abs%sub-add-01: ⊦ i + (j - i0) = i + j - i0; from specification int-abs%sub-eq: ⊦ i - j = i0 ↔ i = i0 + j; 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%neg-15: ⊦ i + ~ j = i - j; from specification int-abs