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Proof step 19 from proof mod-mult-law (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ 0 < j → (i + i0 * j) |%| j = i |%| j
Proof step 21:
0 < j, i = i |%| j + j * j0, i0 = i0 |%| j + j * j1, 0 < j ⊦ (i * i0) |%| j = (i * (i0 - j * j1)) |%| j, j = 0

Rule argument

spec: int-mod inst: name: mod-mult-add seq: ⊦ 0 < j → (i + i0 * j) |%| j = i |%| j subst: [j, i0, i] → [j, ~ j0 * (i0 - j * j1), i * (i0 - j * j1)] flags: rewrite, current

Additional information

Used terms: j, ~ j0 * (i0 - j * j1), i * (i0 - j * j1)