Theorems · Theorem · field theory
Subfield.closure_eq
∀ {K : Type u} [inst : DivisionRing K] (s : Subfield K), Subfield.closure ↑s = sClosure of a subfield S equals S.
- Defined in
- Mathlib.Algebra.Field.Subfield.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coestatement · cited by 8,199
- DivisionRingstatement and proof · cited by 1,062
- Subfieldstatement and proof · cited by 303
- Subfield.closurestatement · cited by 39
- GaloisInsertion.l_u_eqproof · cited by 37
- Subfield.giproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- IntermediateField.sSup_toSubfieldproof · cited by 1
- Field.fg_iff_fg_top_botproof · cited by 1
- IntermediateField.sup_toSubfieldproof · cited by 1
- Subfield.closure_univproof · cited by 0