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Proof step 5 from proof gcd-a (previous step)

⊦ gcd(m, gcd(n, n0)) | gcd(gcd(m, n), n0)

User applied rule insert lemma

And obtained the following new goals

Proof step 6:
⊦ n0 | m ∧ n0 | n → n0 | gcd(m, n)
Proof step 7:
gcd(m, gcd(n, n0)) | gcd(m, n) ∧ gcd(m, gcd(n, n0)) | n0 → gcd(m, gcd(n, n0)) | gcd(gcd(m, n), n0) ⊦ gcd(m, gcd(n, n0)) | gcd(gcd(m, n), n0)

Rule argument

spec: inst: name: gcd-alldiv seq: ⊦ n0 | m ∧ n0 | n → n0 | gcd(m, n) subst: [n0, m, n] → [gcd(m, gcd(n, n0)), gcd(m, n), n0] flags: current, []

Additional information

Used terms: gcd(m, gcd(n, n0)), gcd(m, n), n0