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Proof step 48 from proof congmod-def-mod-02 (previous step)

j ≠ 0, i % j < 0, i < 0, i0 < 0 ⊦ i % j + abs(j) = i0 |%| abs(j) ↔ i |%| j = i0 |%| j, j = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 49:
i < 0, i0 < 0, i % j < 0 ⊦ i % j + abs(j) = i0 |%| abs(j) ↔ i |%| j = i0 |%| j, j = 0

Rule argument

Additional information

Used simplifier rules: forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs