Theorems · Theorem · commutative algebra
IsCoprime.add_mul_left_right
∀ {R : Type u} [inst : CommRing R] {x y : R}, IsCoprime x y → ∀ (z : R), IsCoprime x (y + x * z)- Defined in
- Mathlib.RingTheory.Coprime.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- IsCoprimestatement and proof · cited by 321
- IsCoprime.symmproof · cited by 22
- isCoprime_commproof · cited by 17
- IsCoprime.add_mul_left_leftproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- IsCoprime.add_mul_left_right_iffproof · cited by 1
- IsCoprime.mul_add_left_rightproof · cited by 1
- Polynomial.Separable.mulproof · cited by 1
- Polynomial.abcproof · cited by 0