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Proof step 7 from proof mod-rec-any (previous step)

¬(0 ≤ i ∧ i < j), 0 < j, i < j ⊦ i |%| j = (i - j) |%| j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
0 < j, i < 0, i < j ⊦ i |%| j = (i - j) |%| j

Rule argument

Additional information

Used simplifier rules: forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%transitivity: ⊦ i < i0 ∧ i0 < i1 → i < i1; (forward) from specification oelem[intlista]%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs