Theorems · Theorem · field theory
Subfield.closure_iUnion
∀ {K : Type u} [inst : DivisionRing K] {ι : Sort u_1} (s : ι → Set K),
Subfield.closure (⋃ i, s i) = ⨆ i, Subfield.closure (s i)- Defined in
- Mathlib.Algebra.Field.Subfield.Basic
- Cited by
- 0 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.
Cites9
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
- Set.iUnionstatement · cited by 2,483
- iSupstatement · cited by 2,415
- DivisionRingstatement and proof · cited by 1,062
- Subfieldstatement · cited by 303
- GaloisInsertion.gcproof · cited by 137
- GaloisConnection.l_iSupproof · cited by 78
- Subfield.closurestatement · cited by 39
- Subfield.giproof · cited by 6
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.