Theorems · Theorem · field theory
RatFunc.natDegree_denom_le_natDegree_minpolyX
∀ {K : Type u_1} [inst : Field K] (f : RatFunc K),
(¬∃ c, f = RatFunc.C c) → f.denom.natDegree ≤ (f.minpolyX ↥K⟮f⟯).natDegree- Cited by
- 0 results in Mathlib
- Foundations
- Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
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Cites14
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
- Setstatement · cited by 53,352
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- IntermediateFieldstatement · cited by 988
- IntermediateField.adjoinstatement and proof · cited by 382
- RatFuncstatement and proof · cited by 301
- RatFunc.denomstatement and proof · cited by 59
- RatFunc.Cstatement and proof · cited by 33
- Polynomial.le_natDegree_of_ne_zeroproof · cited by 14
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