Theorems · Theorem · commutative algebra
IsCoprime.map
∀ {R : Type u} [inst : CommSemiring R] {x y : R},
IsCoprime x y → ∀ {S : Type v} [inst_1 : CommSemiring S] (f : R →+* S), IsCoprime (f x) (f y)- Defined in
- Mathlib.RingTheory.Coprime.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses no axioms
- Assumes
- CommSemiringCommSemiring
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.
- DFunLike.coestatement and proof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement and proof · cited by 10,189
- IsCoprimestatement and proof · cited by 321
- RingHom.map_oneproof · cited by 76
- RingHom.map_mulproof · cited by 45
- RingHom.map_addproof · cited by 16
Cited by2
Results whose statement or proof uses this declaration.
- ne_zero_or_ne_zero_of_nat_coprimeproof · cited by 0
- Polynomial.isCoprime_expandproof · cited by 0