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Proof step 10 from proof modmod-mult-02 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
0 < j, 0 ≤ i ⊦ (i % j * i0 % j) % j = (i * i0) % j

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs% ⊦ i < j ↔ ¬ j ≤ i; (ss)