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Proof step 12 from proof prod-div-less (previous step)

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

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: i0 * i1 < i0 * j

Additional information

Used simplifier rules: ⊦ 0 < i → (i * j < i * j0 ↔ j < j0); (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i < j → (j ≤ i ↔ false); (as)%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