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Proof step 3 from proof modmod-mult-09 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
j < 0 ⊦ (i % j * i0) % 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%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%lst-01: ⊦ ¬ i < j → (i ≠ j ↔ j < i); from specification int-basic1