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Proof step 6 from proof mod-pot-shift-pos (previous step)

0 < j, 0 < i0, ∀ i1, j, i. i→n(i1) < i→n(i0) → 0 < j ∧ 0 < i1 → i1 = 0 ∨ (i % j) ^ i1 % j = i ^ i1 % j ⊦ i0 = 0, (i % j) ^ i0 % j = i ^ i0 % j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ 0 < i → j ^ i = j ^ i -1 * j
Proof step 8:
0 < i0, 0 < j, 0 < i0, ∀ i1, j, i. i→n(i1) < i→n(i0) → 0 < j ∧ 0 < i1 → i1 = 0 ∨ (i % j) ^ i1 % j = i ^ i1 % j ⊦ i0 = 0, ((i % j) ^ i0 -1 * i % j) % j = i ^ i0 % j

Rule argument

spec: inst: name: Pot-pos seq: ⊦ 0 < i → j ^ i = j ^ i -1 * j subst: [i, j] → [i0, i % j] flags: rewrite, current

Additional information

Used terms: i0, i % j