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Proof step 21 from proof modmod-add-zero (previous step)

(i + j0) % j = 0, j0 < j, 0 < j, 0 ≤ j0, 0 ≤ i1 ⊦ (i + i1 * j + j0) % j = 0, 0 = j, 0 ≤ i, i ≤ 0 ∧ i1 * j + j0 ≤ 0

User applied rule cut formula

And obtained the following new goals

Proof step 22:
i + i1 * j + j0 = i1 * j + i + j0, (i + j0) % j = 0, j0 < j, 0 < j, 0 ≤ j0, 0 ≤ i1 ⊦ (i + i1 * j + j0) % j = 0, 0 = j, 0 ≤ i, i ≤ 0 ∧ i1 * j + j0 ≤ 0

Rule argument

fma: i + i1 * j + j0 = i1 * j + i + j0

Additional information

Used simplifier rules: 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 + i1 * j + j0 = i1 * j + i + j0