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Proof step 23 from proof ex-modeq-half (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
i0 % j < 0, j / 2 < i0 % j + j, 0 < j, odd(j), i0 % j + j / 2 < 0, i0 % j + j / 2 < j ⊦ ∃ i. ≡mod(i, i0, j) ∧ abs(i) ≤ j / 2

Rule argument

Additional information

Used simplifier rules: add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%mod-lsz: ⊦ 0 < j → ¬ j + i % j < 0; from specification int-div