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Proof step 16 from proof div-eq-same-01 (previous step)

i = i * j + j0, abs(j0) < j, 0 < j, i < 0, j0 < j, j0 ≤ 0 ⊦ j = 0, j = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ i = (* i1) * i + j0 ↔ 0 = (i1 - 1) * i + j0
Proof step 18:
0 = (j - 1) * i + j0, j0 < j, i < 0, 0 < j, abs(j0) < j, j0 ≤ 0 ⊦ j = 1, j = 0

Rule argument

spec: int-mult name: numeq-04 seq: ⊦ i = (* i1) * i + j0 ↔ 0 = (i1 - 1) * i + j0 subst: [j0, i1, i] → [j0, j, i] flags: <all paths>

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: j0, j, i