Theorems · Theorem · field theory
RatFunc.mk_eq_div
∀ {K : Type u} [inst : CommRing K] [inst_1 : IsDomain K] (p q : Polynomial K),
RatFunc.mk p q = (algebraMap (Polynomial K) (RatFunc K)) p / (algebraMap (Polynomial K) (RatFunc K)) q- Defined in
- Mathlib.FieldTheory.RatFunc.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapstatement and proof · cited by 4,706
- IsDomainstatement and proof · cited by 2,196
- RatFuncstatement and proof · cited by 301
- FractionRingproof · cited by 200
- RatFunc.mkstatement · cited by 21
- RatFunc.mk_eq_div'proof · cited by 4
- RatFunc.ofFractionRing_algebraMapproof · cited by 2
- RatFunc.ofFractionRing_divproof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- RatFunc.induction_onproof · cited by 9
- RatFunc.ofFractionRing_mk'proof · cited by 2
- RatFunc.mk_eq_mk'proof · cited by 2
- RatFunc.liftOn_divproof · cited by 1
- RatFunc.laurentAux_algebraMapproof · cited by 1
- RatFunc.algebraMap_applyproof · cited by 0
- RatFunc.div_smulproof · cited by 0