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Proof step 6 from proof modneqp (previous step)

0 < i1, 0 < j, i < i1, j0 < j, j1 < j, 0 ≤ j, 0 ≤ i, i0 ≤ j, 0 ≤ i0, 0 ≤ j0, 0 ≤ j1, i1 * j + j1 ≤ i * i0 + j0 ⊦

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: i1 * j + j1 ≤ i * j + j0

Additional information

Used simplifier rules: ls-forward: ⊦ i * j < i * j0 → i ≠ 0;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%ls-pos: ⊦ 0 < i → (i * j < i * j0 ↔ j < j0);% ⊦ i ≤ j ↔ ¬ j < i; (ss)%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs% ⊦ i + j < i + i0 ↔ j < i0; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i ≠ j → (i ≤ j ↔ i < j); (s)% ⊦ i ≤ j → (j < i ↔ false); (as) Used formulas: i1 * j + j1 ≤ i * j + j0