Theorems · Theorem · field theory
Polynomial.card_roots_le_one_of_irreducible
∀ {R : Type u} [inst : CommRing R] [inst_1 : IsDomain R] {p : Polynomial R}, Irreducible p → p.roots.card ≤ 1- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
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.natDegreeproof · cited by 1,105
- Irreduciblestatement and proof · cited by 496
- Multiset.cardstatement and proof · cited by 375
- Polynomial.rootsstatement and proof · cited by 264
- Polynomial.natDegree_eq_of_degree_eq_someproof · cited by 42
- Polynomial.card_roots'proof · cited by 9
- Polynomial.degree_eq_one_of_irreducible_of_rootproof · cited by 7
- Multiset.empty_or_exists_memproof · cited by 5
- Polynomial.isRoot_of_mem_rootsproof · cited by 2
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