Theorems · Theorem · commutative algebra
IsCoprime.add_mul_left_left
∀ {R : Type u} [inst : CommRing R] {x y : R}, IsCoprime x y → ∀ (z : R), IsCoprime (x + y * z) y- Defined in
- Mathlib.RingTheory.Coprime.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 16 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
- mul_negproof · cited by 590
- IsCoprimestatement and proof · cited by 321
- add_neg_cancel_rightproof · cited by 65
- IsCoprime.of_add_mul_left_leftproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- IsCoprime.add_mul_left_rightproof · cited by 4
- IsCoprime.add_mul_right_leftproof · cited by 4
- IsCoprime.mul_add_left_leftproof · cited by 2
- IsCoprime.add_mul_left_left_iffproof · cited by 2
- IsPrimitiveRoot.argproof · cited by 0
- IsCoprime.add_one_sub_one_of_two_dvdproof · cited by 0