Theorems · Theorem · field theory
IntermediateField.exists_finset_of_mem_iSup
∀ {F : Type u_1} [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] {ι : Type u_3}
{f : ι → IntermediateField F E} {x : E}, x ∈ ⨆ i, f i → ∃ s, x ∈ ⨆ i ∈ s, f i- Cited by
- 3 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- iSupstatement and proof · cited by 2,415
- IntermediateFieldstatement and proof · cited by 988
- IntermediateField.adjoinproof · cited by 382
- IntermediateField.adjoin_simple_isCompactElementproof · cited by 2
- CompleteLattice.IsCompactElement.exists_finset_of_le_iSupproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- IntermediateField.exists_finset_of_mem_supr'proof · cited by 1
- IntermediateField.exists_finset_of_mem_adjoinproof · cited by 0
- IntermediateField.exists_finset_of_mem_supr''proof · cited by 0