Theorems · Theorem · field theory

IntermediateField.adjoinRootEquivAdjoin_symm_apply_gen

∀ (F : Type u_1) [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] {α : E} (h : IsIntegral F α),
  (IntermediateField.adjoinRootEquivAdjoin F h).symm (IntermediateField.AdjoinSimple.gen F α) =
    AdjoinRoot.root (minpoly F α)

Defined in: Mathlib.FieldTheory.IntermediateField.Adjoin.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites16

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement · cited by 62,936
Setstatement · cited by 53,352
Algebrastatement and proof · cited by 11,388
Fieldstatement and proof · cited by 7,404
AlgEquivstatement · cited by 1,681
IntermediateFieldstatement · cited by 988
AlgEquiv.symmstatement · cited by 615
minpolystatement · cited by 439
IsIntegralstatement and proof · cited by 427
IntermediateField.adjoinstatement and proof · cited by 382
AdjoinRootstatement · cited by 177
AdjoinRoot.rootstatement · cited by 77

Cited by1

Results whose statement or proof uses this declaration.

Field.nonempty_algHom_of_exists_rootproof · cited by 3