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

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

User applied rule case distinction

And obtained the following new goals

Proof step 28:
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

Rule argument

pos: right 1

Additional information

Used simplifier rules: forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; (s)% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ i < j → ¬ j < i; (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i ≤ j → (j ≤ i ↔ i = j); (s)% ⊦ i < 0 ∧ 0 ≤ j → i < j; (s)% ⊦ i < j → (j ≤ i ↔ false); (as)