Theorems · Theorem · field theory
IntermediateField.subset_adjoin
∀ (F : Type u_1) [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] (S : Set E),
S ⊆ ↑(IntermediateField.adjoin F S)- Cited by
- 59 results in Mathlib
- Foundations
- Depth 78 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
- SetLike.coestatement · cited by 8,199
- Fieldstatement and proof · cited by 7,404
- IntermediateFieldstatement · cited by 988
- IntermediateField.adjoinstatement · cited by 382
- Subfield.subset_closureproof · cited by 15
Cited by59
Results whose statement or proof uses this declaration.
- IntermediateField.mem_adjoin_simple_selfproof · cited by 19
- IsCyclotomicExtension.isGaloisproof · cited by 13
- IntermediateField.adjoin_selfproof · cited by 6
- IntermediateField.adjoin_univproof · cited by 6
- IntermediateField.algebra_adjoin_le_adjoinproof · cited by 6
- IntermediateField.adjoin_mapproof · cited by 5
- IntermediateField.adjoin_eq_adjoin_pow_expChar_pow_of_isSeparableproof · cited by 4
- IntermediateField.LinearDisjoint.lift_adjoin_rank_eq_lift_rank_right_of_isAlgebraicstatement and proof · cited by 4
- IsSeparable.of_algebra_isSeparable_of_isSeparableproof · cited by 3
- Algebra.FormallyEtale.of_isSeparableproof · cited by 3
- Field.nonempty_algHom_of_exists_rootproof · cited by 3