Theorems · Theorem · commutative algebra
isCoprime_mul_unit_left_left
∀ {R : Type u_1} [inst : CommSemiring R] {x : R}, IsUnit x → ∀ (y z : R), IsCoprime (x * y) z ↔ IsCoprime y z- Defined in
- Mathlib.RingTheory.Coprime.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- IsUnitstatement and proof · cited by 1,602
- IsCoprimestatement and proof · cited by 321
- isCoprime_group_smul_leftproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- isCoprime_mul_unit_right_leftproof · cited by 1
- isCoprime_mul_units_leftproof · cited by 1
- Polynomial.resultant_eq_zero_iffproof · cited by 0