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Proof step 16 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 → (i % j) ^ i1 % j = i ^ i1 % j ∨ i1 = 0 ⊦ ((i % j) ^ i2 % j * i % j) % j = (i ^ i2 * i) % j, ~1 = i2, 0 = j, 0 < j ∧ 0 < i2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
0 < j, ∀ i1, j, i. i→n(i1) < i→n(0 + 1) → 0 < j ∧ 0 < i1 → (i % j) ^ i1 % j = i ^ i1 % j ∨ i1 = 0 ⊦ (1 % j * i % j) % j = i % j, 0 = 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% ⊦ 1 * i = i; (s)% ⊦ i ≤ j → (j ≤ i ↔ i = j); (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)