Theorems · Theorem · field theory
Polynomial.zero_of_eval_zero
∀ {R : Type u} [inst : CommRing R] [IsDomain R] [Infinite R] (p : Polynomial R),
(∀ (x : R), Polynomial.eval x p = 0) → p = 0- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Polynomialstatement and proof · cited by 5,681
- IsDomainstatement and proof · cited by 2,196
- Polynomial.evalstatement and proof · cited by 796
- Infinitestatement and proof · cited by 352
- Polynomial.rootsproof · cited by 264
- Multiset.toFinsetproof · cited by 230
- Multiset.mem_toFinsetproof · cited by 39
- Polynomial.mem_rootsproof · cited by 30
- Fintype.falseproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.funextproof · cited by 2
- Polynomial.eq_zero_of_forall_eval_zero_of_natDegree_lt_cardproof · cited by 2