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Proof step 3 from proof modzero-02 (previous step)

i < j, i < i * j + j0, i < 0, j0 < j, 0 < j, i + 1 < j, 0 ≤ i * j + j0 ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 4:
i + 1 < j, 0 < j, j0 < j, i < 0, i < i * j + j0, i < j, 0 ≤ i * j + j0, 0 ≤ (i + 1) * j ⊦

Rule argument

fma: 0 ≤ (i + 1) * j

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% ⊦ i ≤ j ↔ ¬ j < i; (ss)%lf-01: ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) from specification int-basic1%trans: ⊦ i < j ∧ j < j0 → i < j0; (forward) from specification int-basic1%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs% ⊦ i + j < i + i0 ↔ j < i0; (s)% ⊦ i < j → ¬ j < i; (s) Used formulas: 0 ≤ (i + 1) * j