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Proof step 5 from proof congmod-def-mod (previous step)

0 < j ⊦ j | i - i0 ↔ i |%| j = i0 |%| j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ i | j ↔ (∃ i0. i * i0 = j)
Proof step 7:
0 < j ⊦ (∃ i1. j * i1 = i - i0) ↔ i |%| j = i0 |%| j

Rule argument

spec: int-gcd inst: name: divides seq: ⊦ i | j ↔ (∃ i0. i * i0 = j) subst: [j, i] → [i - i0, j] flags: rewrite

Additional information

Used terms: i - i0, j