Theorems · Theorem · commutative algebra
isCoprime_comm
∀ {R : Type u} [inst : CommSemiring R] {x y : R}, IsCoprime x y ↔ IsCoprime y x- Defined in
- Mathlib.RingTheory.Coprime.Basic
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses no axioms
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- IsCoprimestatement · cited by 321
- IsCoprime.symmproof · cited by 22
Cited by17
Results whose statement or proof uses this declaration.
- IsCoprime.of_add_mul_left_rightproof · cited by 5
- IsCoprime.of_mul_right_leftproof · cited by 4
- IsCoprime.add_mul_left_rightproof · cited by 4
- isCoprime_zero_rightproof · cited by 4
- IsCoprime.mul_rightproof · cited by 2
- DirichletCharacter.apply_ne_zero_iffproof · cited by 2
- isCoprime_group_smul_rightproof · cited by 2
- IsCoprime.abs_right_iffproof · cited by 2
- ZMod.coe_int_isUnit_iff_isCoprimeproof · cited by 2
- IsCoprime.add_mul_right_rightproof · cited by 2
- IsCoprime.sub_one_right_of_dvdproof · cited by 1
- Nat.forall_exists_prime_gt_and_zmodEqproof · cited by 1