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Proof step 22 from proof mod-pot-shift-pos (previous step)

i2 = 0 ∨ (i % j) ^ i2 % j = i ^ i2 % j, 0 < j, 0 ≤ i2, ∀ i1, j, i. i→n(i1) < i→n(i2 + 1) → 0 < j ∧ 0 < i1 → i1 = 0 ∨ (i % j) ^ i1 % j = i ^ i1 % j ⊦ i2 = 0, 0 = j, ~1 = i2, ((i % j) ^ i2 % j * i % j) % j = (i ^ i2 * i) % j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
(i % j) ^ i2 % j = i ^ i2 % j, 0 < j, 0 < i2, ∀ i1, j, i. i→n(i1) < i→n(i2 + 1) → 0 < j ∧ 0 < i1 → i1 = 0 ∨ (i % j) ^ i1 % j = i ^ i1 % j ⊦ i2 = 0, 0 = j, ~1 = i2, (i ^ i2 % j * i % j) % j = (i ^ i2 * i) % j

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs