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Proof step 8 from proof modmod-add-04 (previous step)

0 < j, j0 < j, 0 ≤ i0, 0 ≤ j0, 0 ≤ i1 ⊦ (j0 + i0 % j) % j = ((i1 * j + j0) + i0) % j

User applied rule cut formula

And obtained the following new goals

Proof step 9:
j0 < j, 0 < j, 0 ≤ i1, 0 ≤ j0, 0 ≤ i0 ⊦ (j0 + i0 % j) % j = ((i1 * j + j0) + i0) % j, i0 < 0

Rule argument

fma: i0 < 0

Additional information

Used simplifier rules: ⊦ i ≤ j → (j < i ↔ false); (as) Used formulas: i0 < 0