Theorems · Theorem · field theory
Polynomial.ne_zero_of_mem_nthRootsFinset
∀ {R : Type u} {n : ℕ} [inst : CommRing R] [inst_1 : IsDomain R] {η a : R},
a ≠ 0 → η ∈ Polynomial.nthRootsFinset n a → η ≠ 0- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 136 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites7
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
- Finsetstatement · cited by 13,712
- IsDomainstatement and proof · cited by 2,196
- zero_powproof · cited by 361
- Polynomial.nthRootsFinsetstatement and proof · cited by 23
- Polynomial.mem_nthRootsFinsetproof · cited by 6
- Polynomial.nthRootsFinset_zeroproof · cited by 4
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