Theorems · Theorem · number theory
Nat.factorization_gcd
∀ {a b : ℕ}, a ≠ 0 → b ≠ 0 → (a.gcd b).factorization = a.factorization ⊓ b.factorization- Defined in
- Mathlib.Data.Nat.Factorization.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsuppstatement and proof · cited by 5,255
- eq_or_neproof · cited by 1,117
- inf_le_leftproof · cited by 286
- inf_le_rightproof · cited by 238
- Finsupp.prodproof · cited by 231
- Nat.factorizationstatement and proof · cited by 215
- zero_dvd_iffproof · cited by 37
- Nat.factorization_le_iff_dvdproof · cited by 18
- Nat.factorization_prod_pow_eq_self_of_le_factorizationproof · cited by 5
- Nat.dvd_prod_pow_of_factorization_leproof · cited by 1
- Nat.prod_pow_dvd_of_le_factorizationproof · cited by 1
- Nat.gcd_greatestproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Nat.factorization_lcmproof · cited by 4
- ArithmeticFunction.IsMultiplicative.lcm_apply_mul_gcd_applyproof · cited by 2