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Proof step 2 from proof mod-pot-pot (previous step)

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

User applied rule induction

And obtained the following new goals

Proof step 3:
0 ≤ i0 ∧ 0 < j, ∀ i1, j, i. i→n(i1) < i→n(i0) → 0 ≤ i1 ∧ 0 < j → (i |%| j) ^ i1 |%| j = i ^ i1 |%| j ⊦ (i |%| j) ^ i0 |%| j = i ^ i0 |%| j

Rule argument

indvar: i→n(i0) wfpred: <

Additional information

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