Theorems · Theorem · field theory
IntermediateField.adjoin_toSubfield
∀ (F : Type u_1) [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] (S : Set E),
(IntermediateField.adjoin F S).toSubfield = Subfield.closure (Set.range ⇑(algebraMap F E) ∪ S)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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 and proof · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapstatement · cited by 4,706
- Set.rangestatement · cited by 4,705
- IntermediateField.adjoinstatement · cited by 382
- Subfieldstatement · cited by 303
- Subfield.closurestatement · cited by 39
- IntermediateField.toSubfieldstatement · cited by 38
Cited by2
Results whose statement or proof uses this declaration.
- IntermediateField.lift_cardinalMk_adjoin_leproof · cited by 2
- IntermediateField.sSup_toSubfieldproof · cited by 1