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Proof step 27 from proof ls-even-01 (previous step)

¬ j ≤ i, i % 2 = 0, j % 2 = 0, i ≤ ~2, i < 0, ¬ j < 0 → (0 < j / 2 + i / 2 ↔ 0 < j + i), j ≤ 0 → (¬ i / 2 ≤ j / 2 ↔ j < i) ⊦ i / 2 < j / 2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: two-even: ⊦ i % 2 = 0 → (i / 2 = j ↔ i = 2 * j);%divmult: j ≠ 0 ⊦ i % j = 0 → i / j * j = i;%succ-01: ⊦ i +1 = i + 1; from specification int-basic2%trans: ⊦ i < j ∧ j < j0 → i < j0; (forward) from specification int-basic1%lf-01: ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs