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Proof step 14 from proof congmod-def-mod-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
0 ≤ i, 0 ≤ i0, 0 ≤ i % abs(j), 0 ≤ i % j ⊦ i % abs(j) = i0 |%| abs(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