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Proof step 63 from proof congmod-def-mod-02 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 64:
i < 0, i0 < 0, i % j < 0, i0 % abs(j) < 0 ⊦ j = 0, i % j = i0 % abs(j) ↔ i % j + j = i0 |%| j

Rule argument

Additional information

Used simplifier rules: 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%add-in: ⊦ i + j = i + i0 ↔ j = i0; from specification int-basic2