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Proof step 8 from proof mod-mult-law (previous step)

i = j * j0 + i |%| j, i0 = j * j1 + i0 |%| j, 0 < j ⊦ (i * i0) |%| j = (i |%| j * i0 |%| j) |%| j, j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ j = i0 + j0 ↔ j - i0 = j0
Proof step 10:
i - j * j0 = i |%| j, i0 = j * j1 + i0 |%| j, 0 < j ⊦ (i * i0) |%| j = (i |%| j * i0 |%| j) |%| j, j = 0

Rule argument

spec: int-abs inst: name: add-rew seq: ⊦ j = i0 + j0 ↔ j - i0 = j0 subst: [j0, i0, j] → [i |%| j, j * j0, i] flags: rewrite

Additional information

Used terms: i |%| j, j * j0, i