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Proof step 2 from proof modzero-06 (previous step)

i < 0, j < j0, j < 0, i * j + j0 ≤ 0 ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 3:
(i + 1) * j < 0, i < 0, j < j0, j < 0, i * j + j0 ≤ 0 ⊦

Rule argument

fma: (i + 1) * j < 0

Additional information

Used simplifier rules: dist-rsplit: ⊦ i * (j + j0) = i * j + i * j0;%one: ⊦ 1 * i = i;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%lep-02: ⊦ i + j ≤ i + j0 ↔ j ≤ j0; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs Used formulas: (i + 1) * j < 0