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Proof step 35 from proof ls-even-01 (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 36:
j % 2 = 0, i % 2 = 0, j < 0, i / 2 < j / 2, j ≤ i, i ≤ 0 → (j / 2 < i / 2 ↔ j < i) ⊦

Rule argument

pos: right 1

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;% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i < j → ¬ j < i; (s)%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1% ⊦ i ≤ j → (j ≤ i ↔ i = j); (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; (s)% ⊦ ¬ i < i; (s)