Theorems · Theorem · group theory
Subspace.biUnion_ne_univ_of_top_notMem
∀ {k : Type u_1} {E : Type u_2} [inst : DivisionRing k] [Infinite k] [inst_2 : AddCommGroup E] [inst_3 : Module k E]
{s : Finset (Subspace k E)}, ⊤ ∉ s → ⋃ p ∈ s, ↑p ≠ Set.univA vector space over an infinite field cannot be a finite union of proper subspaces.
- Defined in
- Mathlib.GroupTheory.CosetCover
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- Finsetstatement and proof · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- Top.topstatement and proof · cited by 9,680
- SetLike.coestatement and proof · cited by 8,199
- Set.univstatement and proof · cited by 3,945
- Finiteproof · cited by 3,029
- Set.iUnionstatement and proof · cited by 2,483
- Nontrivialproof · cited by 2,416
- HasQuotient.Quotientproof · cited by 2,301
- DivisionRingstatement and proof · cited by 1,062
Cited by1
Results whose statement or proof uses this declaration.
- Subspace.top_mem_of_biUnion_eq_univproof · cited by 1