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Proof step 66 from proof congmod-def-mod-02 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 67:
i < 0, i0 < 0, i % j < 0, i0 % j < 0 ⊦ i % j = i0 % j ↔ i % j + 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