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Proof step 2 from proof mod-add-both-zero (previous step)

i % j = 0, i0 % j = 0 ⊦ (i + i0) % j = 0, 0 = j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
j ≠ 0 ⊦ i % j = 0 ↔ (∃ j0. i = j0 * j)
Proof step 4:
j ≠ 0, i % j = 0, ∃ j0. i0 = j0 * j ⊦ (i + i0) % j = 0, 0 = j

Rule argument

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

Additional information

Used terms: j, i0