Theorems · Theorem · field theory
IntermediateField.algHomAdjoinIntegralEquiv_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} {K : Type u}
[inst_3 : Field K] [inst_4 : Algebra F K] (h : IsIntegral F α) (x : { x // x ∈ (minpoly F α).aroots K }),
((IntermediateField.algHomAdjoinIntegralEquiv F h).symm x) (IntermediateField.AdjoinSimple.gen F α) = ↑x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Equivstatement · cited by 8,337
- Fieldstatement and proof · cited by 7,404
- Polynomialproof · cited by 5,681
- Equiv.symmstatement · cited by 3,681
- AlgHomstatement · cited by 3,236
- Multisetstatement · cited by 2,627
- IntermediateFieldstatement · cited by 988
- Polynomial.aevalproof · cited by 615
- minpolystatement and proof · cited by 439
Cited by2
Results whose statement or proof uses this declaration.
- IntermediateField.exists_algHom_adjoin_of_splits_of_aevalproof · cited by 1
- Normal.of_isSplittingFieldproof · cited by 0