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Proof step 5 from proof modmod-mult-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
j < 0 ⊦ (i % j * i0 % j) % j = (i * i0) % j

Rule argument

Additional information

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