Theorems · Theorem · field theory
RatFunc.algebraMap_injective
∀ (K : Type u) [inst : CommRing K] [inst_1 : IsDomain K], Function.Injective ⇑(algebraMap (Polynomial K) (RatFunc K))
- Defined in
- Mathlib.FieldTheory.RatFunc.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapstatement · cited by 4,706
- IsDomainstatement and proof · cited by 2,196
- RatFuncstatement and proof · cited by 301
- FractionRingproof · cited by 200
- IsFractionRing.injectiveproof · cited by 70
- RatFunc.ofFractionRing_injectiveproof · cited by 3
- RatFunc.ofFractionRing_comp_algebraMapproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- RatFunc.num_mul_eq_mul_denom_iffproof · cited by 3
- RatFunc.transcendental_Xproof · cited by 2
- RatFunc.C_injectiveproof · cited by 0