Theorems · Theorem · combinatorics
Hindman.exists_FS_of_finite_cover
∀ {M : Type u_1} [inst : AddSemigroup M] [Nonempty M] (s : Set (Set M)),
s.Finite → ⊤ ⊆ ⋃₀ s → ∃ c ∈ s, ∃ a, Hindman.FS a ⊆ cThe weak form of Hindman's theorem: in any finite cover of a nonempty additive semigroup, one of the parts contains an FS-set.
- Defined in
- Mathlib.Combinatorics.Hindman
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddSemigroupNonempty
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Top.topstatement and proof · cited by 9,680
- Set.Finitestatement and proof · cited by 1,814
- Set.sUnionstatement and proof · cited by 392
- Filter.mem_of_supersetproof · cited by 308
- Stream'statement and proof · cited by 205
- Ultrafilterproof · cited by 193
- AddSemigroupstatement and proof · cited by 136
- Filter.univ_memproof · cited by 96
- Hindman.FSstatement and proof · cited by 11
- Ultrafilter.finite_sUnion_mem_iffproof · cited by 5
- Ultrafilter.continuous_add_leftproof · cited by 2
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.