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Proof step 3 from proof modmod-mult-05 (previous step)

j0 < 0 ⊦ (i % (j * j0)) % j = i % j, j0 = 0, j = 0

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: modmod-mult-03 seq: j ≠ 0 ⊦ 0 < j0 → (i % (j * j0)) % j = i % j subst: [j, j0, i] → [j, ~ j0, i] flags: current, []

Additional information

Used simplifier rules: mod-neg: j ≠ 0 ⊦ i % ~ j = i % j;%neg: ⊦ 0 < ~ i ↔ i < 0; from specification int-abs%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%minus-left: ⊦ ~ i * j = ~(i * j); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%zero-neq: ⊦ i < 0 → (i * j = 0 ↔ j = 0); from specification int-mult Used terms: j, ~ j0, i