Theorems · Theorem · field theory
minpoly.natDegree_le_spanFinrank
∀ (A : Type u_1) {B : Type u_2} [inst : CommRing A] [inst_1 : Ring B] [inst_2 : Algebra A B] [Module.Finite A B]
(x : B), (minpoly A x).natDegree ≤ ⊤.spanFinrank- Defined in
- Mathlib.FieldTheory.Minpoly.Finite
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Top.topstatement and proof · cited by 9,680
- Ringstatement and proof · cited by 7,463
- Submodulestatement · cited by 7,192
- Polynomialproof · cited by 5,681
- map_zeroproof · cited by 1,614
- Polynomial.natDegreestatement and proof · cited by 1,105
- Module.Finitestatement and proof · cited by 1,032
- Module.Endproof · cited by 774
- Polynomial.aevalproof · cited by 615
Cited by1
Results whose statement or proof uses this declaration.
- minpoly.natDegree_leproof · cited by 6