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Proof step 8 from proof mod-neq (previous step)

i * j = i * j0 + j1, i < j1, i < 0, i < ~1, j1 + i < 0, 0 < j1, i + 1 < j1 ⊦

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: modeqp-02 seq: i * j + j0 = i0 * j + j1, j < 0, 0 ≤ j0, j0 < abs(j), 0 ≤ j1, j1 < abs(j) ⊦ i = i0 ∧ j0 = j1 subst: [i, j, j0, i0, j1] → [j, i, 0, j0, j1] flags: current, []

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i;%eq-neg: ⊦ i < 0 → (i * j = i * j0 ↔ j = j0);%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%add-zero-rev: ⊦ 0 + i = i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%abs-08: ⊦ i < 0 → abs(i) = ~ i; from specification int-abs%neg: ⊦ 0 < ~ i ↔ i < 0; from specification int-abs%neg-07: ⊦ i < ~ j ↔ i + j < 0; from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1 Used terms: j, i, 0, j0, j1