Theorems · Theorem · number theory
Int.dvd_of_dvd_mul_left_of_gcd_one
∀ {a b c : ℤ}, a ∣ b * c → a.gcd c = 1 → a ∣ bEuclid's lemma: if a ∣ b * c and gcd a c = 1 then a ∣ b.
Compare with IsCoprime.dvd_of_dvd_mul_left and
UniqueFactorizationMonoid.dvd_of_dvd_mul_left_of_no_prime_factors
- Defined in
- Mathlib.Data.Int.GCD
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- zero_addproof · cited by 2,366
- mul_assocproof · cited by 1,667
- dvd_mul_leftproof · cited by 47
- Int.gcdBproof · cited by 7
- Int.gcdAproof · cited by 7
- Int.gcd_eq_gcd_abproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Int.dvd_of_dvd_mul_right_of_gcd_oneproof · cited by 2