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Proof step 4 from proof abs-num (previous step)

⊦ rational(abs(rational(i, i0).num), rational(i, i0).denom).num = abs(rational(i, i0).num)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ i ≠ 0 ∧ 0 < j → rational(i, j).num = i / gcd(i, j)
Proof step 6:
abs(rational(i, i0).num) ≠ 0 ∧ 0 < rational(i, i0).denom ⊦ abs(rational(i, i0).num) / gcd(abs(rational(i, i0).num), rational(i, i0).denom) = abs(rational(i, i0).num)

Rule argument

name: numerator-pos rotate: F subst: [j, i] → [rational(i, i0).denom, abs(rational(i, i0).num)]

Additional information

Used simplifier rules: denom-pos-01: ⊦ ¬ rj.denom ≤ 0;%num-zero-denum-one: ⊦ rj.num = 0 → rj.denom = 1;%numerator-zero: ⊦ rational(0, j).num = 0;% ⊦ abs(i) = 0 ↔ i = 0;% ⊦ ¬ i < j ↔ j ≤ i; Used terms: rational(i, i0).denom, abs(rational(i, i0).num)