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Proof step 7 from proof mod-rec-neg (previous step)

i0 * j + j < 0, i0 < j, i0 < 0, 0 < j ⊦ 0 = (i0 * j + j) |%| j

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: numsucc seq: ⊦ (* i0) * i + i = (i0 + 1) * i subst: [i, i0] → [j, i0] flags: rewrite

Additional information

Used simplifier rules: mod-mult-01: ⊦ 0 < j → (i * j) |%| j = 0;%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: j, i0