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Proof step 24 from proof modmod-mult-07 (previous step)

i0 < j, i0 < 0, 0 ≤ i, 0 < j, i0 + 1 < j ⊦ ~(i % j * ~ i0) % j = (i * i0) % j

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: mod-neg-01 seq: j ≠ 0 ⊦ ~ i % j = ~(i % j) subst: [j, i] → [j, i % j * ~ i0] flags: rewrite, current

Additional information

Used simplifier rules: 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%neg-02: ⊦ ~ ~ i = i; from specification int-abs%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs Used terms: j, i % j * ~ i0