Theorems · Theorem · commutative algebra
IsCoprime.of_add_mul_left_left
∀ {R : Type u} [inst : CommSemiring R] {x y z : R}, IsCoprime (x + y * z) y → IsCoprime x y- Defined in
- Mathlib.RingTheory.Coprime.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses no axioms
- Assumes
- CommSemiring
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.
- CommSemiringstatement and proof · cited by 10,911
- mul_commproof · cited by 2,262
- add_commproof · cited by 1,535
- mul_addproof · cited by 413
- IsCoprimestatement and proof · cited by 321
- mul_left_commproof · cited by 184
- add_left_commproof · cited by 76
Cited by5
Results whose statement or proof uses this declaration.
- IsCoprime.add_mul_left_leftproof · cited by 6
- IsCoprime.of_add_mul_left_rightproof · cited by 5
- IsCoprime.of_add_mul_right_leftproof · cited by 2
- IsCoprime.add_mul_left_left_iffproof · cited by 2
- IsCoprime.of_mul_add_left_leftproof · cited by 1