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Proof step 12 from proof mod-mult-add (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
0 < j, i0 ≤ 0, i0 < j ⊦ (i + i0 * j) |%| j = i |%| j

Rule argument

Additional information

Used simplifier rules: forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs