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Proof step 38 from proof ex-modeq-half (previous step)

¬(j ≤ j0 * j + j ∧ 0 < j), i0 % j = j0 * j + j, 0 ≤ i0 % j, j / 2 < i0 % j, 0 < j, odd(j) ⊦ j = 0, (i0 % j - j) |%| j = i0 % j ∧ j ≤ i0 % j + j / 2, ∃ i. ≡mod(i, i0, j) ∧ abs(i) ≤ j / 2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (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%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%zero-ge: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); from specification int-mult%lep: ⊦ i ≤ i + j ↔ 0 ≤ j; from specification int-abs