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Proof step 5 from proof div-am-rew (previous step)

j0 < j, 0 ≤ i, 0 ≤ i0, 0 < j, 0 ≤ j0, 0 ≤ i2 ⊦ (i + i0 * (i2 * j + j0)) / j = (i + i0 * j0) / j + i0 * i2

User applied rule cut formula

And obtained the following new goals

Proof step 6:
i + i0 * (i2 * j + j0) = (i + i0 * j0) + i0 * i2 * j, j0 < j, 0 ≤ i, 0 ≤ i0, 0 < j, 0 ≤ j0, 0 ≤ i2 ⊦ (i + i0 * (i2 * j + j0)) / j = (i + i0 * j0) / j + i0 * i2

Rule argument

fma: i + i0 * (i2 * j + j0) = (i + i0 * j0) + i0 * i2 * j

Additional information

Used simplifier rules: add-in: ⊦ i + j = i + i0 ↔ j = i0; from specification int-basic2%eq-dist: ⊦ (i + j) * i0 = j0 + j * i0 ↔ i * i0 = j0; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used formulas: i + i0 * (i2 * j + j0) = (i + i0 * j0) + i0 * i2 * j