Theorems · Theorem · field theory
Polynomial.finite_setOfPred_isRoot
∀ {R : Type u} [inst : CommRing R] [IsDomain R] {p : Polynomial R}, p ≠ 0 → {x | p.IsRoot x}.Finite- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 7 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
- Set.ofPredstatement and proof · cited by 6,101
- Polynomialstatement and proof · cited by 5,681
- IsDomainstatement and proof · cited by 2,196
- Set.Finitestatement and proof · cited by 1,814
- Polynomial.rootsproof · cited by 264
- Multiset.toFinsetproof · cited by 230
- Finset.finite_toSetproof · cited by 210
- Polynomial.IsRootstatement · cited by 152
- Polynomial.mem_rootsproof · cited by 30
Cited by7
Results whose statement or proof uses this declaration.
- Polynomial.eventually_atTop_not_isRootproof · cited by 3
- Polynomial.eq_zero_of_infinite_isRootproof · cited by 2
- Polynomial.eventually_cofinite_not_isRootproof · cited by 1
- Polynomial.eventually_atBot_not_isRootproof · cited by 0
- Polynomial.exists_max_rootproof · cited by 0
- Polynomial.exists_min_rootproof · cited by 0
- Polynomial.finite_setOf_isRootproof · cited by 0