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Proof step 28 from proof ls-even-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
i % 2 = 0, j % 2 = 0, 0 < j / 2 + i / 2 ↔ 0 < j + i, i < 0, i < j, 0 < j, j / 2 ≤ i / 2 ⊦

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;%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs% ⊦ i < j → ¬ j < i; (s)%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult% ⊦ i ≤ j → (j ≤ i ↔ i = j); (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i ≤ j ↔ ¬ j < i; (ss)