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Proof step 3 from proof modmod-add-04 (previous step)

0 < j, 0 ≤ i0, 0 ≤ i ⊦ (i % j + i0 % j) % j = (i + i0) % j

User applied rule cut formula

And obtained the following new goals

Proof step 4:
0 < j, 0 ≤ i, 0 ≤ i0 ⊦ (i % j + i0 % j) % j = (i + i0) % j, i < 0

Rule argument

fma: i < 0

Additional information

Used simplifier rules: ⊦ i ≤ j → (j < i ↔ false); (as) Used formulas: i < 0