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Proof step 15 from proof mod-pot-shift-pos (previous step)

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 ⊦ 0 < j ∧ 0 < i2, 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 16:
0 < j, ∀ i1, j, i. i→n(i1) < i→n(0 + 1) → 0 < j ∧ 0 < i1 → i1 = 0 ∨ (i % j) ^ i1 % j = i ^ i1 % j ⊦ 0 = j, (1 % j * i % j) % j = i % j

Rule argument

Additional information

Used simplifier rules: Pot-zero: ⊦ j ^ 0 = 1;%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%one: ⊦ 1 * i = i; from specification int-mult%anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs