Theorems · Theorem · field theory
IntermediateField.biSup_adjoin_simple
∀ {F : Type u_1} [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] (S : Set E),
⨆ x ∈ S, F⟮x⟯ = IntermediateField.adjoin F S- Cited by
- 4 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- iSupstatement and proof · cited by 2,415
- IntermediateFieldstatement and proof · cited by 988
- IntermediateField.adjoinstatement and proof · cited by 382
- GaloisConnection.l_iSupproof · cited by 78
- Set.biUnion_of_singletonproof · cited by 43
- iSup_subtype''proof · cited by 18
- IntermediateField.gcproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- IntermediateField.finiteDimensional_adjoinproof · cited by 7
- IntermediateField.isAlgebraic_adjoinproof · cited by 2
- IntermediateField.adjoin_finset_isCompactElementproof · cited by 1
- IntermediateField.exists_finset_of_mem_adjoinproof · cited by 0