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Proof step 7 from proof modmod-add-04 (previous step)

j0 < j, 0 < 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 8:
j0 < j, 0 < j, 0 ≤ i0, 0 ≤ j0, 0 ≤ i1 ⊦ i0 < 0, (j0 + i0 % j) % j = ((i1 * j + j0) + i0) % j

Rule argument

fma: i0 < 0

Additional information

Used simplifier rules: lels-04: ⊦ i ≤ j → (¬ ¬ j < i ↔ false); from specification int-abs Used formulas: i0 < 0