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Proof step 20 from proof num-neg-03 (previous step)

gcd(i, j) = 1, 0 < j ⊦ (rational(0, 1) - rational(i, j)).num + i = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ 0 < j1 ∧ 0 < j2 → rational(i1, j1) - rational(i2, j2) = rational(i1, j1) + rational(~ i2, j2)
Proof step 22:
0 < 1 ∧ 0 < j, gcd(i, j) = 1, 0 < j ⊦ (rational(0, 1) + rational(~ i, j)).num + i = 0

Rule argument

name: sub-def-01 rotate: F subst: [j2, i2, j1, i1] → [j, i, 1, 0]

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: j, i, 1, 0