Theorems · Theorem · field theory
IntermediateField.adjoin.mono
∀ (F : Type u_1) [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] (S T : Set E),
S ⊆ T → IntermediateField.adjoin F S ≤ IntermediateField.adjoin F T- Cited by
- 9 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- IntermediateFieldstatement · cited by 988
- IntermediateField.adjoinstatement · cited by 382
- GaloisConnection.monotone_lproof · cited by 76
- IntermediateField.gcproof · cited by 5
Cited by9
Results whose statement or proof uses this declaration.
- IntermediateField.adjoin_adjoin_leftproof · cited by 6
- Field.Emb.Cardinal.strictMono_leastExtproof · cited by 2
- Field.Emb.Cardinal.strictMono_filtrationproof · cited by 1
- IntermediateField.Lifts.union_isExtendibleproof · cited by 1
- IntermediateField.adjoin_adjoin_rightproof · cited by 1
- Field.Emb.Cardinal.adjoin_image_leastExtproof · cited by 1
- RatFunc.IntermediateField.adjoin_Xproof · cited by 0
- IntermediateField.extendScalars_adjoinproof · cited by 0