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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)

Rule argument

spec: nat-prime inst: name: gcd-rec2 seq: ⊦ m ≤ n → gcd(m, n) = gcd(m, n - m) subst: [n, m] → [m + n, n] flags: rewrite, current

Additional information

Used simplifier rules: gcd-sym: ⊦ gcd(m, n) ≠ gcd(n, m) ↔ false;%gcd-a: ⊦ gcd(m, gcd(n, n0)) = gcd(gcd(m, n), n0);%eq-01: ⊦ m + n - m = n; from specification nat%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat%l-02: ⊦ ¬ m + n < m; from specification nat-basic2 Used terms: m + n, n