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Proof step 5 from proof ls-even-01 (previous step)

i % 2 = 0, j % 2 = 0 ⊦ i / 2 < j / 2 ↔ i < j, 0 ≤ i ∧ 0 ≤ j

User applied rule insert lemma

And obtained the following new goals

Proof step 6:
⊦ i % 2 = 0 ∧ j % 2 = 0 ∧ 0 ≤ i ∧ 0 ≤ j → (i / 2 < j / 2 ↔ i < j)
Proof step 7:
i % 2 = 0 ∧ ~ j % 2 = 0 ∧ 0 ≤ i ∧ 0 ≤ ~ j → (i / 2 < ~ j / 2 ↔ i < ~ j), i % 2 = 0, j % 2 = 0 ⊦ i / 2 < j / 2 ↔ i < j, 0 ≤ i ∧ 0 ≤ j

Rule argument

spec: int-div inst: name: ls-even seq: ⊦ i % 2 = 0 ∧ j % 2 = 0 ∧ 0 ≤ i ∧ 0 ≤ j → (i / 2 < j / 2 ↔ i < j) subst: [i, j] → [i, ~ j] flags: current, []

Additional information

Used terms: i, ~ j