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Proof step 7 from proof abs-num (previous step)

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), rational(i, i0).num = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ gcd(i, j) = gcd(abs(i), abs(j))
Proof step 9:
0 < rational(i, i0).denom ⊦ abs(rational(i, i0).num) / gcd(abs(abs(rational(i, i0).num)), abs(rational(i, i0).denom)) = abs(rational(i, i0).num), rational(i, i0).num = 0

Rule argument

seq: ⊦ gcd(i, j) = gcd(abs(i), abs(j)) subst: [j, i] → [rational(i, i0).denom, abs(rational(i, i0).num)] rotate: F spec: int-gcd inst: name: gcd-pos-01

Additional information

Used terms: rational(i, i0).denom, abs(rational(i, i0).num)