Theorems · Theorem · field theory
IntermediateField.adjoin_simple_isCompactElement
∀ {F : Type u_1} [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] (x : E),
IsCompactElement F⟮x⟯Adjoining a single element is compact in the lattice of intermediate fields.
- Cited by
- 2 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.
Cites16
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
- Set.Elemproof · cited by 7,166
- Set.Nonemptyproof · cited by 2,627
- iSupproof · cited by 2,415
- IntermediateFieldstatement and proof · cited by 988
- IntermediateField.adjoinstatement and proof · cited by 382
- SetLike.mem_coeproof · cited by 302
- DirectedOnproof · cited by 271
- Set.mem_iUnionproof · cited by 212
- Set.Nonempty.to_subtypeproof · cited by 55
Cited by2
Results whose statement or proof uses this declaration.
- IntermediateField.exists_finset_of_mem_iSupproof · cited by 3
- IntermediateField.adjoin_finset_isCompactElementproof · cited by 1