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Proof step 8 from proof mod-pot-shift-pos (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
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

Additional information

Used simplifier rules: sub-pred: ⊦ i -1 = i - 1; from specification int-abs