Theorems · Theorem · field theory
Subfield.coe_sInf
∀ {K : Type u} [inst : DivisionRing K] (S : Set (Subfield K)), ↑(sInf S) = ⋂ s ∈ S, ↑s- Defined in
- Mathlib.Algebra.Field.Subfield.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- SetLike.coestatement and proof · cited by 8,199
- Set.imageproof · cited by 5,609
- Set.iInterstatement and proof · cited by 1,084
- DivisionRingstatement and proof · cited by 1,062
- InfSet.sInfstatement and proof · cited by 935
- Subringproof · cited by 602
- Subfieldstatement and proof · cited by 303
- Set.iInter_congr_Propproof · cited by 170
- Set.iInter_existsproof · cited by 44
- Subfield.toSubringproof · cited by 23
- Set.biInter_and'proof · cited by 17
Cited by5
Results whose statement or proof uses this declaration.
- IntermediateField.sInf_toSubfieldproof · cited by 1
- Subfield.mem_sInfproof · cited by 1
- Subfield.coe_iInfproof · cited by 1
- Subfield.isGLB_sInfproof · cited by 0
- IntermediateField.iInf_toSubfieldproof · cited by 0