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Proof step 3 from proof cong-mult (previous step)

¬ 0 < j ⊦ ≡mod(j0 * j + i, i0, j) ↔ ≡mod(i, i0, j)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
j ≤ 0 ⊦ ≡mod(j0 * j + i, i0, j) ↔ ≡mod(i, i0, j)

Rule argument

Additional information

Used simplifier rules: forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs