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Proof step 2 from proof ls-def (previous step)

0 < j, 0 < j0 ⊦ (rational(i, j) - rational(i0, j0)).num < 0 ↔ ¬ i0 * j ≤ i * j0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 0 < j1 ∧ 0 < j2 → rational(i1, j1) - rational(i2, j2) = rational(i1, j1) + rational(~ i2, j2)
Proof step 4:
0 < j ∧ 0 < j0, 0 < j, 0 < j0 ⊦ (rational(i, j) + rational(~ i0, j0)).num < 0 ↔ ¬ i0 * j ≤ i * j0

Rule argument

name: sub-def-01 rotate: F subst: [j2, i2, j1, i1] → [j0, i0, j, i]

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: j0, i0, j, i