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Proof step 13 from proof modeq-neg-02 (previous step)

j * (i1 + i0) + j1 = i2 * j + j0, abs(j0) < j, 0 ≤ i1 * j + j1, 0 < j, 1 < j, 0 < j1, i0 < 0, j1 < j, j0 ≤ 0, j0 < j, j0 < j1, i2 * j + j0 < 0, j0 ≤ j1, j0 + j < j1 ⊦ (i1 + i0 + 1) * j + (j1 - j0 - j) = i2 * j + 0 ∧ 0 ≤ j1 - j0 - j ∧ j1 - j0 - j < j ∧ 0 ≤ 0, j1 = j0 + j, j1 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%add-mult-two: ⊦ i + i = 2 * i; from specification int-mult%sub-ls: ⊦ i - j < i0 ↔ i < j + i0; from specification int-abs%sub-le-01: ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; from specification int-abs%eq-succ-01: ⊦ (i + i0) * j + j0 = (i + i1) * j + j1 ↔ i0 * j + j0 = i1 * j + j1; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%succ-rmerge: ⊦ i * j + i = i * (j + 1); from specification int-mult%sub-eq: ⊦ i - j = i0 ↔ i = i0 + j; from specification int-abs%add-zero: ⊦ i + 0 = i; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%sub-add-01: ⊦ i + (j - i0) = i + j - i0; from specification int-abs%sub-sub: ⊦ i - j - i0 = i - j + i0; from specification int-abs