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Theorems · Theorem · field theory

Subfield.closure_sUnion

∀ {K : Type u} [inst : DivisionRing K] (s : Set (Set K)), Subfield.closure (⋃₀ s) = ⨆ t ∈ s, Subfield.closure t
Defined in
Mathlib.Algebra.Field.Subfield.Basic
Cited by
1 results in Mathlib
Foundations
Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DivisionRing
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IntermediateField.sSup_toSubfield · cited by 1IntermediateField.sSup_to…Set · cited by 53352SetiSup · cited by 2415iSupDivisionRing · cited by 1062DivisionRingSet.sUnion · cited by 392Set.sUnionSubfield · cited by 303SubfieldGaloisInsertion.gc · cited by 137GaloisInsertion.gcSubfield.closure · cited by 39Subfield.closureGaloisConnection.l_sSup · cited by 19GaloisConnection.l_sSupSubfield.gi · cited by 6Subfield.giSubfield.closure_sUnionCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.