Theorems · Theorem · commutative algebra
isCoprime_group_smul_left
∀ {R : Type u_1} {G : Type u_2} [inst : CommSemiring R] [inst_1 : Group G] [inst_2 : MulAction G R]
[SMulCommClass G R R] [IsScalarTower G R R] (x : G) (y z : R), IsCoprime (x • y) z ↔ IsCoprime y z- Defined in
- Mathlib.RingTheory.Coprime.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Groupstatement and proof · cited by 6,238
- IsScalarTowerstatement and proof · cited by 3,896
- SMulCommClassstatement and proof · cited by 1,927
- one_smulproof · cited by 1,374
- MulActionstatement and proof · cited by 1,294
- IsCoprimestatement and proof · cited by 321
- inv_mul_cancelproof · cited by 107
- smul_mul_assocproof · cited by 77
- mul_smul_commproof · cited by 65
- smul_mul_smul_commproof · cited by 14
Cited by3
Results whose statement or proof uses this declaration.
- isCoprime_mul_unit_left_leftproof · cited by 3
- isCoprime_group_smul_rightproof · cited by 2
- isCoprime_group_smulproof · cited by 0