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Proof step 1 from proof modmod-mult-05 (conclusion)

⊦ j ≠ 0 ∧ j0 ≠ 0 → (i % (j * j0)) % j = i % j

User applied rule cut formula

And obtained the following new goals

Proof step 2:
j0 < 0 ⊦ j ≠ 0 ∧ j0 ≠ 0 → (i % (j * j0)) % j = i % j

Rule argument

fma: j0 < 0

Additional information

Used simplifier rules: modmod-mult-03: j ≠ 0 ⊦ 0 < j0 → (i % (j * j0)) % j = i % j;%lst-01: ⊦ ¬ i < j → (i ≠ j ↔ j < i); from specification int-basic1%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used formulas: j0 < 0