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Proof step 5 from proof mod-abs-neg-div (previous step)

j < 0, j < j0, 0 < j0 ⊦ j = 0, (j0 * j) |%| ~ j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mod inst: name: mod-pos-def seq: ⊦ 0 ≤ i % j → i |%| j = i % j subst: [j, i] → [~ j, j0 * j] flags: rewrite, current

Additional information

Used simplifier rules: mod-neg: j ≠ 0 ⊦ i % ~ j = i % j; from specification int-div%mod-mult-04: j ≠ 0 ⊦ (i * j) % j = 0; from specification int-div%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: ~ j, j0 * j