Theorems · Theorem · field theory
Subfield.closure_union
∀ {K : Type u} [inst : DivisionRing K] (s t : Set K), Subfield.closure (s ∪ t) = Subfield.closure s ⊔ Subfield.closure t- Defined in
- Mathlib.Algebra.Field.Subfield.Basic
- Cited by
- 2 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.
Cites7
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
- DivisionRingstatement and proof · cited by 1,062
- Subfieldstatement · cited by 303
- GaloisInsertion.gcproof · cited by 137
- GaloisConnection.l_supproof · cited by 81
- Subfield.closurestatement · cited by 39
- Subfield.giproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Field.fg_iff_fg_top_botproof · cited by 1
- IntermediateField.sup_toSubfieldproof · cited by 1