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Proof step 13 from proof modmod-mult-03 (previous step)

0 < j0 ⊦ (i % (j * j0)) % j = i % j, j = 0, j < 0, 0 < j ∧ 0 ≤ i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
0 < j0, 0 < j, i < 0 ⊦ (i % (j * j0)) % j = i % j

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ i < j → ¬ j < i; (s)% ⊦ ¬ i < j → (i = j ↔ ¬ j < i); (ss)