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Proof step 11 from proof transitivity (previous step)

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

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: i * j0 * j1 < i0 * j * j1

Additional information

Used simplifier rules: ⊦ 0 < i → (i * j < i * j0 ↔ j < j0);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i * j = j * i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ i * j * j0 = (i * j) * j0; Used formulas: i * j0 * j1 < i0 * j * j1