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Proof step 6 from proof zero-gr-add-02 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 7:
i1 * j + i1 = i1 * (j + 1), 0 < i1 * j + i1, i1 * j + i0 ≤ i1 * j + i1, 0 ≤ i0, 0 < i1 * j + i0, i0 ≤ i1, j + 1 < i1 * j + i0, j < i1 * j + i0, j < 0, 0 < i1, j + 1 < i1 ⊦ i1 = 0

Rule argument

fma: i1 * j + i1 = i1 * (j + 1)

Additional information

Used simplifier rules: eq-dist: ⊦ (i + j) * i0 = j0 + j * i0 ↔ i * i0 = 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 Used formulas: i1 * j + i1 = i1 * (j + 1)