Theorems · Theorem · commutative algebra
IsCoprime.symm
∀ {R : Type u} [inst : CommSemiring R] {x y : R}, IsCoprime x y → IsCoprime y x- Defined in
- Mathlib.RingTheory.Coprime.Basic
- Cited by
- 22 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.
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
- add_commproof · cited by 1,535
- IsCoprimestatement and proof · cited by 321
Cited by22
Results whose statement or proof uses this declaration.
- isCoprime_commproof · cited by 17
- IsCoprime.add_mul_left_rightproof · cited by 4
- Int.ModEq.pow_card_sub_one_eq_oneproof · cited by 3
- IsCoprime.neg_rightproof · cited by 3
- Complex.isPrimitiveRoot_exp_of_isCoprimeproof · cited by 2
- IsCoprime.add_mul_right_rightproof · cited by 2
- IsCoprime.wronskian_eq_zero_iffproof · cited by 1
- exists_sum_eq_one_iff_pairwise_coprimeproof · cited by 1
- Int.eq_pow_of_mul_eq_pow_odd_rightproof · cited by 1
- Polynomial.div_eq_quo_add_rem_div_add_rem_divproof · cited by 1
- Polynomial.quo_mul_prod_add_sum_rem_mul_prod_uniqueproof · cited by 1
- RatFunc.irreducible_minpolyX'proof · cited by 1