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Proof step 2 from proof gcd-le (previous step)

⊦ n = 0, m ≠ 0 → gcd(m, n) ≤ m

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
⊦ m ≠ 0 ∧ n ≠ 0 → gcd(m, n) ≤ m ∧ gcd(m, n) ≤ n

Rule argument

spec: nat-prime inst: name: gcd-le-both seq: ⊦ m ≠ 0 ∧ n ≠ 0 → gcd(m, n) ≤ m ∧ gcd(m, n) ≤ n subst: [m, n] → [m, n] flags: current, []

Additional information

Used simplifier rules: lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat%ls-le-simp: ⊦ m < n → (n ≤ m ↔ false); from specification nat Used terms: m, n