Theorems · Theorem · field theory
Subfield.mem_sInf
∀ {K : Type u} [inst : DivisionRing K] {S : Set (Subfield K)} {x : K}, x ∈ sInf S ↔ ∀ p ∈ S, x ∈ p- Defined in
- Mathlib.Algebra.Field.Subfield.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 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.
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
- SetLike.coeproof · cited by 8,199
- DivisionRingstatement and proof · cited by 1,062
- InfSet.sInfstatement and proof · cited by 935
- Subfieldstatement and proof · cited by 303
- Set.ext_iffproof · cited by 90
- Subfield.coe_sInfproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Subfield.mem_closureproof · cited by 2