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Proof step 14 from proof ex-modeq-half (previous step)

¬ 0 ≤ i0 % j, odd(j), 0 < j, j / 2 < abs(i0 |%| j), i0 |%| j < j ⊦ ∃ i. ≡mod(i, i0, j) ∧ abs(i) ≤ j / 2, (i0 |%| j - j) |%| j = i0 |%| j ∧ j ≤ i0 |%| j + j / 2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
i0 % j < 0, i0 |%| j < j, j / 2 < abs(i0 |%| j), 0 < j, odd(j) ⊦ (i0 |%| j - j) |%| j = i0 |%| j ∧ j ≤ i0 |%| j + j / 2, ∃ i. ≡mod(i, i0, j) ∧ abs(i) ≤ j / 2

Rule argument

Additional information

Used simplifier rules: mod-less-01: ⊦ 0 < j → i % j < j; from specification int-div%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%transitivity: ⊦ i < i0 ∧ i0 < i1 → i < i1; (forward) from specification oelem[intlista]%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs