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Proof step 5 from proof modmod-mult-07 (previous step)

0 < j, i < 0 ⊦ (i % j * i0) % j = (i * i0) % j, 0 ≤ i ∧ 0 ≤ i0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ i < j → (j ≤ i ↔ false); (as)% ⊦ i < 0 ∧ 0 ≤ j → i < j; (s)%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs