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Proof step 3 from proof mod-mult-add (previous step)

0 < i0, 0 < j ⊦ (i + i0 * j) |%| j = i |%| j

User applied rule induction

And obtained the following new goals

Proof step 4:
0 < i0 ∧ 0 < j, ∀ i1, j, i. i→n(i1) < i→n(i0) → 0 < i1 ∧ 0 < j → (i + i1 * j) |%| j = i |%| j ⊦ (i + i0 * j) |%| j = i |%| j

Rule argument

indvar: i→n(i0) wfpred: <

Additional information

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