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Proof step 2 from proof mod-pred-neg (previous step)

i < 0, 0 < j ⊦ i % j = (i - 1) % j + 1, i % j - 1 = ~ j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
0 < j, i < 0 ⊦ i % j = (i - 1) % j + 1, 1 = i % j + 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%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ i + ~ j = i - j; (s)% ⊦ i - j = i0 ↔ i = i0 + j; (s)