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Proof step 32 from proof ex-modeq-half (previous step)

0 < j ∧ i0 % j - j < 0, odd(j), 0 < j, j / 2 < i0 % j, 0 ≤ i0 % j, (i0 % j - j) % j = 0 ⊦ ∃ 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 33:
(i0 % j - j) % j = 0, 0 ≤ i0 % j, j / 2 < 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: lel: ⊦ i < i0 ∧ i = i1 → i1 < i0; (forward) from specification oelem[intlista]%mod-less-01: ⊦ 0 < j → i % j < j; from specification int-div%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%ax-04: ⊦ i + 0 = i; from specification int-basic2%sub-ls: ⊦ i - j < i0 ↔ i < j + i0; from specification int-abs