Theorems · Theorem · field theory
IntermediateField.sSup_toSubfield
∀ {F : Type u_1} [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E]
(S : Set (IntermediateField F E)), S.Nonempty → (sSup S).toSubfield = sSup (IntermediateField.toSubfield '' S)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- SetLike.coeproof · cited by 8,199
- Fieldstatement and proof · cited by 7,404
- Set.imagestatement and proof · cited by 5,609
- Algebra.algebraMapproof · cited by 4,706
- Set.rangeproof · cited by 4,705
- Set.Nonemptystatement and proof · cited by 2,627
- DivisionRingproof · cited by 1,062
- IntermediateFieldstatement and proof · cited by 988
- SupSet.sSupstatement and proof · cited by 954
Cited by1
Results whose statement or proof uses this declaration.
- IntermediateField.iSup_toSubfieldproof · cited by 0