Theorems · Theorem · field theory
Polynomial.eq_zero_of_forall_eval_zero_of_natDegree_lt_card
∀ {R : Type u} [inst : CommRing R] [IsDomain R] (f : Polynomial R),
(∀ (r : R), Polynomial.eval r f = 0) → ↑f.natDegree < Cardinal.mk R → f = 0- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Fintypeproof · cited by 7,736
- Polynomialstatement and proof · cited by 5,681
- Finiteproof · cited by 3,029
- Cardinalstatement · cited by 2,598
- IsDomainstatement and proof · cited by 2,196
- Polynomial.natDegreestatement and proof · cited by 1,105
- Cardinal.mkstatement and proof · cited by 942
- Polynomial.evalstatement and proof · cited by 796
- Infiniteproof · cited by 352
- Fintype.ofFiniteproof · cited by 255
- Cardinal.mk_fintypeproof · cited by 81
Cited by2
Results whose statement or proof uses this declaration.
- LieAlgebra.engel_isBot_of_isMinproof · cited by 1
- Polynomial.exists_eval_ne_zero_of_natDegree_lt_cardproof · cited by 0