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Proof step 19 from proof div-add1-negpos-neg-01 (previous step)

i1 * j + i2 * j + j0 = i0 * j + j1, i0 + 1 < j, j1 + 1 < j, 2 + i0 * j + j1 < j, i0 * j + j1 < j0, i0 * j + j1 < j, i0 * j + j1 < 0, i0 < j0, i0 < j, i0 ≤ 0, j1 < j0, j1 < j, j1 ≤ 0, 2 + i1 * j + i2 * j < j, i1 * j + i2 * j < 0, i1 + 1 < j0, j + i1 * j < j0, 0 ≤ i2 * j + j0, i1 * j + i2 * j < ~1, 0 < j0, j0 < j, i1 < j, i1 < 0, j + i1 * j ≤ 0, 1 < j, 0 < j, 0 ≤ i2, i1 < j0, 2 + i1 < j, (i1 * j + i2 * j) + 1 < j0, i1 * j + i2 * j < j0, i1 * j + i2 * j < j, i1 * j < j0, abs(j1) < j, (i0 * j + j1) + 1 < j0, j1 ≤ j0 ⊦ i0 = i1 + i2 + 1, j = 1, j0 = 0, j0 < j1 + j ∧ (i2 * j + i1 * j) + j0 = i0 * j + j1, (i2 * j + i1 * j) + j0 = i0 * j + j1 ∧ j1 + j ≤ j0 ∧ j0 < 2 * j + j1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
i1 * j + i2 * j + j0 = i0 * j + j1, i1 * j < j1, i1 < j + j1, i1 + 1 < j + j1, i1 * j + i2 * j < j + j1, (i1 * j + i2 * j) + 1 < j + j1, i0 < j + j1, j1 < 0, j1 + 1 < j0, 0 < j + j1, i1 * j + i2 * j < j, i1 * j + i2 * j < j0, 2 + i1 < j, i1 < j0, 0 ≤ i2, 0 < j, 1 < j, j + i1 * j ≤ 0, i1 < 0, i1 < j, j0 < j, 0 < j0, i1 * j + i2 * j < ~1, 0 ≤ i2 * j + j0, j + i1 * j < j0, i1 * j + i2 * j < 0, 2 + i1 * j + i2 * j < j, j1 < j, j1 < j0, i0 ≤ 0, i0 < j, i0 < j0, i0 * j + j1 < 0, i0 * j + j1 < j, i0 * j + j1 < j0, 2 + i0 * j + j1 < j, i0 + 1 < j, 2 * j + j1 < j, 2 * j + j1 ≤ j0, j1 + j ≤ j0, j1 ≤ j0, (i0 * j + j1) + 1 < j0, i1 * j < j0, i1 + 1 < j0, (i1 * j + i2 * j) + 1 < j0, 2 + j1 < j ⊦ j0 = 0, j = 1, i0 = i1 + i2 + 1

Rule argument

Additional information

Used simplifier rules: zero-ls: ⊦ 0 < i → (i * j < 0 ↔ j < 0); from specification int-mult%lst-04: ⊦ i + j < i0 ∧ j0 < j → i + j0 < i0; from specification int-basic2%modzero-02: ⊦ i < 0 ∧ j0 < j ∧ 0 < j → i * j + j0 < 0; from specification int-mult%lsone: ⊦ i < 1 ↔ i ≤ 0; from specification int-abs%ls-same: ⊦ 0 < i → (i * j < i ↔ j < 1); from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%ls-add: ⊦ 0 ≤ j1 ∧ j1 < j → (i0 * j + j1 < j ↔ i0 ≤ 0); from specification int-mult%ls-01: ⊦ i + j < i + i0 ↔ j < i0; from specification int-basic2%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%add-less: ⊦ 0 < i → i1 < i1 + i; from specification int-basic2%ls-add-both: ⊦ i < j → i1 + i < i1 + j; from specification int-basic2%succ-01: ⊦ i +1 = i + 1; from specification int-basic2%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%trans: ⊦ i < j ∧ j < j0 → i < j0; (forward) from specification int-basic1%lf-01: ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%zero-gels-03: ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%neg-13: ⊦ ~ i < j ↔ 0 < j + i; from specification int-abs%abs-08: ⊦ i < 0 → abs(i) = ~ i; from specification int-abs%ls: ⊦ i + j < j ↔ i < 0; from specification int-basic2%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; 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