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Proof step 1 from proof gcd-add (conclusion)

⊦ gcd(n, m + n) = gcd(m, n)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ m ≤ n → gcd(m, n) = gcd(m, n - m)
Proof step 3:
n ≤ m + n ⊦ gcd(n, m + n - n) = gcd(m, n)

Rule argument

spec: <toplevel> name: gcd-rec2 seq: ⊦ m ≤ n → gcd(m, n) = gcd(m, n - m) subst: [n, m] → [m + n, n] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ m + n < m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: m + n, n