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Proof step 6 from proof cong-mult (previous step)

j ≤ 0 ⊦ j | abs(j0 * j + i - i0) ↔ ≡mod(i, i0, j)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
j ≤ 0 ⊦ j | j0 * j + i - i0 ↔ ≡mod(i, i0, j)

Rule argument

Additional information

Used simplifier rules: div-abs-02: ⊦ i | abs(j) ↔ i | j; from specification int-gcd