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Proof step 2 from proof modlsp (previous step)

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

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: j * i < j * (i0 + 1)

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%lst-01: ⊦ i < j + i0 ∧ j < j0 → i < j0 + i0; from specification int-basic2 Used formulas: j * i < j * (i0 + 1)