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Proof step 9 from proof mods-nls (previous step)

0 < i, j < 0, 0 < j + j * i ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 10:
j + j * i = j * (i + 1), 0 < j + j * i, j < 0, 0 < i ⊦

Rule argument

fma: j + j * i = j * (i + 1)

Additional information

Used simplifier rules: dist-lsplit: ⊦ (i + i0) * j = i * j + i0 * j;%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% ⊦ i + j = i + i0 ↔ j = i0; (s) Used formulas: j + j * i = j * (i + 1)