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Proof step 26 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 27:
odd(j), 0 < j, j / 2 < i0 % j, 0 ≤ i0 % j ⊦ ∃ i. ≡mod(i, i0, j) ∧ abs(i) ≤ j / 2, (i0 % j - j) |%| j = i0 % j ∧ j ≤ i0 % j + j / 2

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%mod-less-01: ⊦ 0 < j → i % j < j; from specification int-div%absle: ⊦ 0 ≤ i → abs(i) = i; from specification int-abs