Theorems · Theorem · combinatorics
Hindman.FP.mul
∀ {M : Type u_1} [inst : Semigroup M] {a : Stream' M} {m : M},
m ∈ Hindman.FP a → ∃ n, ∀ m' ∈ Hindman.FP (Stream'.drop n a), m * m' ∈ Hindman.FP aIf m and m' are finite products in M, then so is m * m', provided that m' is obtained
from a subsequence of M starting sufficiently late.
- Defined in
- Mathlib.Combinatorics.Hindman
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- Semigroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- mul_assocproof · cited by 1,667
- Stream'statement and proof · cited by 205
- Semigroupstatement and proof · cited by 202
- Stream'.tailproof · cited by 68
- Stream'.headproof · cited by 43
- Stream'.dropstatement and proof · cited by 30
- Hindman.FPstatement and proof · cited by 11
- Hindman.FP.tailproof · cited by 4
- Hindman.FP.consproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Hindman.exists_idempotent_ultrafilter_le_FPproof · cited by 1