Theorems · Theorem · number theory
IsRelPrime.mul_left
∀ {α : Type u_1} [inst : CommMonoid α] {x y z : α} [DecompositionMonoid α],
IsRelPrime x z → IsRelPrime y z → IsRelPrime (x * y) z- Defined in
- Mathlib.Algebra.Divisibility.Units
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidstatement and proof · cited by 2,264
- Dvd.dvd.transproof · cited by 148
- IsRelPrimestatement and proof · cited by 136
- dvd_mul_rightproof · cited by 89
- dvd_mul_leftproof · cited by 47
- DecompositionMonoidstatement and proof · cited by 39
- IsUnit.mulproof · cited by 32
- exists_dvd_and_dvd_of_dvd_mulproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- IsRelPrime.prod_leftproof · cited by 2
- IsRelPrime.mul_left_iffproof · cited by 1
- IsRelPrime.mul_rightproof · cited by 1