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Proof step 1 from proof congmod-def-mod-01 (conclusion)

⊦ 0 ≤ i ∧ 0 ≤ i0 ∧ j ≠ 0 → (≡mod(i, i0, j) ↔ i |%| j = i0 |%| j)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
0 ≤ i, 0 ≤ i0 ⊦ ≡mod(i, i0, j) ↔ i |%| j = i0 |%| j, j = 0

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs