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Proof step 8 from proof congmod-def-mod (previous step)

i |%| j = i0 |%| j, 0 < j ⊦ ∃ i1. i = j * i1 + i0

User applied rule insert lemma

And obtained the following new goals

Proof step 9:
⊦ j ≠ 0 → (∃ j0. i = j * j0 + i |%| j)
Proof step 10:
j ≠ 0 → (∃ j0. i0 = j * j0 + i0 |%| j), i |%| j = i0 |%| j, 0 < j ⊦ ∃ i1. i = j * i1 + i0

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