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Proof step 11 from proof prod-div-less (previous step)

i0 * i1 = i0 * j + j0, 0 ≤ i1, 0 ≤ i0, 0 ≤ j0, j0 < j, 1 < j, 0 < j, 0 < i1, 0 < i0, i1 < j, i0 < j ⊦

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: i0 * i1 < i0 * j

Additional information

Used simplifier rules: ls-pos: ⊦ 0 < i → (i * j < i * j0 ↔ j < j0); from specification int-mult%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used formulas: i0 * i1 < i0 * j