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Proof step 2 from proof modzero-04 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 3:
(i + 1) * j < 0, i * j + j0 < 0, i < 0, j < j0, j < 0 ⊦

Rule argument

fma: (i + 1) * j < 0

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-04: ⊦ i + j < i0 ∧ j0 < j → i + j0 < i0; from specification int-basic2 Used formulas: (i + 1) * j < 0