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theorem proved term proof

gcd_mul_lcm

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formal statement (Lean)

  23theorem gcd_mul_lcm (a b : ℕ) : Nat.gcd a b * Nat.lcm a b = a * b := by

proof body

Term-mode proof.

  24  exact Nat.gcd_mul_lcm a b
  25
  26/-! ### Casted lcm formulas (for analytic work) -/
  27
  28/-- A casted form of `gcd_mul_lcm`:
  29\[
  30(\gcd(a,b) : \mathbb{Q}) \cdot (\operatorname{lcm}(a,b) : \mathbb{Q}) = (a b : \mathbb{Q}).
  31\]
  32-/

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