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Proof step 5 from proof mod-mult-law (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Proof step 6:
⊦ j ≠ 0 → (∃ j0. i = j * j0 + i |%| j)
Proof step 7:
j ≠ 0 → (∃ j0. i0 = j * j0 + i0 |%| j), i = j * j0 + i |%| j, 0 < j ⊦ (i * i0) |%| j = (i |%| j * i0 |%| j) |%| j, j = 0

Rule argument

spec: int-mod inst: name: mod-ex-div seq: ⊦ j ≠ 0 → (∃ j0. i = j * j0 + i |%| j) subst: [j, i] → [j, i0] flags: current, []

Additional information

Used terms: j, i0