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

0 ≤ j, 0 < j0 ⊦ (i + i0 * j ^ j0) % j = 0 ↔ i % j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 0 < i → j ^ i = j ^ i -1 * j
Proof step 4:
0 < j0, 0 ≤ j, 0 < j0 ⊦ (i + i0 * j ^ j0 -1 * j) % j = 0 ↔ i % j = 0

Rule argument

spec: inst: name: Pot-pos seq: ⊦ 0 < i → j ^ i = j ^ i -1 * j subst: [i, j] → [j0, j] flags: rewrite, current

Additional information

Used terms: j0, j