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Proof step 17 from proof add-div-mult (previous step)

j1 < j, j0 < j, 0 < j, 0 ≤ j0, 0 ≤ i1, 0 ≤ j1, 0 ≤ i2, 0 ≤ j0 + i2 * j + j1, (j0 + j1) / j = 1 ∨ (j0 + j1) / j = 0 ⊦ i2 + (j0 + j1) / j = (j0 + i2 * j + j1) / j

User applied rule cut formula

And obtained the following new goals

Proof step 18:
j0 + i2 * j + j1 = j * i2 + j0 + j1, j1 < j, j0 < j, 0 < j, 0 ≤ j0, 0 ≤ i1, 0 ≤ j1, 0 ≤ i2, 0 ≤ j0 + i2 * j + j1, (j0 + j1) / j = 1 ∨ (j0 + j1) / j = 0 ⊦ i2 + (j0 + j1) / j = (j0 + i2 * j + j1) / j

Rule argument

fma: j0 + i2 * j + j1 = j * i2 + j0 + j1

Additional information

Used simplifier rules: 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: j0 + i2 * j + j1 = j * i2 + j0 + j1