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Proof step 7 from proof gcd-rec2 (previous step)

⊦ gcd(n0 + m, m) = gcd(m, n0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ n ≤ m → gcd(m, n) = gcd(m - n, n)
Proof step 9:
m ≤ n0 + m ⊦ gcd(n0 + m - m, m) = gcd(m, n0)

Rule argument

spec: <toplevel> name: gcd-rec1 seq: ⊦ n ≤ m → gcd(m, n) = gcd(m - n, n) subst: [n, m] → [m, n0 + m] 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, n0 + m