Theorems · Theorem · field theory
RatFunc.finrank_eq_max_natDegree
∀ {K : Type u_1} [inst : Field K] (f : RatFunc K),
Module.finrank (↥K⟮f⟯) (RatFunc K) = max f.num.natDegree f.denom.natDegree- Cited by
- 1 results in Mathlib
- Foundations
- Depth 144 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.
Cites41
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Fieldstatement and proof · cited by 7,404
- Polynomialproof · cited by 5,681
- Bot.botproof · cited by 4,720
- mul_commproof · cited by 2,262
- Module.finrankstatement and proof · cited by 1,770
- Polynomial.Cproof · cited by 1,598
- Polynomial.natDegreestatement and proof · cited by 1,105
- Module.Finiteproof · cited by 1,032
- IntermediateFieldstatement and proof · cited by 988
- Polynomial.leadingCoeffproof · cited by 498
Cited by1
Results whose statement or proof uses this declaration.
- RatFunc.Luroth.eq_adjoin_generatorproof · cited by 0