Theorems · Theorem · field theory
Polynomial.valuation_X_eq_neg_one
∀ (K : Type u_1) [inst : Field K], (IsDedekindDomain.HeightOneSpectrum.valuation (RatFunc K) (Polynomial.idealX K)) RatFunc.X = WithZero.exp (-1)
- Defined in
- Mathlib.FieldTheory.RatFunc.AsPolynomial
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement · cited by 5,681
- Polynomial.Xproof · cited by 1,639
- Multiplicativestatement and proof · cited by 875
- Valuationstatement · cited by 823
- WithZerostatement and proof · cited by 586
- RatFuncstatement and proof · cited by 301
- IsDedekindDomain.HeightOneSpectrum.valuationstatement and proof · cited by 130
- WithZero.expstatement and proof · cited by 112
- RatFunc.Xstatement · cited by 58
- IsDedekindDomain.HeightOneSpectrum.valuation_of_algebraMapproof · cited by 23
Cited by2
Results whose statement or proof uses this declaration.
- RatFunc.valuation_surjectiveproof · cited by 2
- LaurentSeries.exists_ratFunc_eq_vproof · cited by 0