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Proof step 5 from proof mod-pot-shift-pos (previous step)

0 < j, 0 < i0 ⊦ (i % j) ^ i0 % j = i ^ i0 % j, i0 = 0

User applied rule induction

And obtained the following new goals

Proof step 6:
0 < j, 0 < i0, ∀ i1, j, i. i→n(i1) < i→n(i0) → 0 < j ∧ 0 < i1 → (i % j) ^ i1 % j = i ^ i1 % j ∨ i1 = 0 ⊦ (i % j) ^ i0 % j = i ^ i0 % j, i0 = 0

Rule argument

indvar: i→n(i0) wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: i→n(i0)