Theorems · Theorem · commutative algebra
natDegree_radical_le
∀ {k : Type u_1} [inst : Field k] [inst_1 : DecidableEq k] {a : Polynomial k},
(UniqueFactorizationMonoid.radical a).natDegree ≤ a.natDegree- Defined in
- Mathlib.RingTheory.Polynomial.Radical
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Polynomial.natDegreestatement and proof · cited by 1,105
- UniqueFactorizationMonoid.radicalstatement · cited by 64
- Polynomial.natDegree_oneproof · cited by 43
- Polynomial.natDegree_le_of_dvdproof · cited by 11
- UniqueFactorizationMonoid.radical_dvd_selfproof · cited by 7
- UniqueFactorizationMonoid.radical_zeroproof · cited by 7
- UniqueFactorizationMonoid.radical.congr_simpproof · cited by 6
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