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Theorems · Theorem · field theory

IntermediateField.gc

∀ {F : Type u_1} [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E],
  GaloisConnection (IntermediateField.adjoin F) fun x => ↑x
Defined in
Mathlib.FieldTheory.IntermediateField.Adjoin.Defs
Cited by
5 results in Mathlib
Foundations
Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldFieldAlgebra
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

IntermediateField.adjoin.mono · cited by 9adjoin.monoIntermediateField.adjoin_union · cited by 5IntermediateField.adjoin_…IntermediateField.biSup_adjoin_simple · cited by 4IntermediateField.biSup_a…IntermediateField.adjoin_iUnion · cited by 1IntermediateField.adjoin_…IntermediateField.isSplittingField_iSup · cited by 0IntermediateField.isSplit…IntermediateField.gi · cited by 0IntermediateField.giSet · cited by 53352SetAlgebra · cited by 11388AlgebraSetLike.coe · cited by 8199SetLike.coeField · cited by 7404FieldIntermediateField · cited by 988IntermediateFieldIntermediateField.adjoin · cited by 382IntermediateField.adjoinGaloisConnection · cited by 253GaloisConnectionIntermediateField.adjoin_le_iff · cited by 28IntermediateField.adjoin_…IntermediateField.gcCITED BYCITES

Cites8

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

Cited by6

Results whose statement or proof uses this declaration.