Theorems · Theorem · field theory

Polynomial.nthRootsFinset.congr_simp

∀ (n n_1 : ℕ),
  n = n_1 →
    ∀ {R : Type u_1} (a a_1 : R),
      a = a_1 →
        ∀ [inst : CommRing R] [inst_1 : IsDomain R], Polynomial.nthRootsFinset n a = Polynomial.nthRootsFinset n_1 a_1

Defined in: Mathlib.Algebra.Polynomial.Roots
Cited by: 2 results in Mathlib
Foundations: Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing IsDomain

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Cites4

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
Polynomial.nthRootsFinsetstatement and proof · cited by 23

Cited by2

Results whose statement or proof uses this declaration.

IsPrimitiveRoot.nthRoots_one_eq_biUnion_primitiveRootsproof · cited by 2
Polynomial.map_mem_nthRootsFinsetproof · cited by 1