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Proof step 15 from proof mod-mult-law (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ (i - j) * j0 = i * j0 - j * j0
Proof step 17:
i = i |%| j + j * j0, i0 = i0 |%| j + j * j1, 0 < j ⊦ (i * i0) |%| j = (i * (i0 - j * j1) - (j * j0) * (i0 - j * j1)) |%| j, j = 0

Rule argument

spec: int-mult inst: name: dist-sub-split seq: ⊦ (i - j) * j0 = i * j0 - j * j0 subst: [j0, j, i] → [i0 - j * j1, j * j0, i] flags: rewrite

Additional information

Used terms: i0 - j * j1, j * j0, i