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Theorems · Theorem · number theory

ThreeAPFree.mono

∀ {α : Type u_2} [inst : AddMonoid α] {s t : Set α}, t ⊆ s → ThreeAPFree s → ThreeAPFree t
Defined in
Mathlib.Combinatorics.Additive.AP.Three.Defs
Cited by
5 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
AddMonoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

threeAPFree_insert · cited by 1threeAPFree_insertIsAddFreimanHom.threeAPFree · cited by 1IsAddFreimanHom.threeAPFr…addRothNumber_union_le · cited by 1addRothNumber_union_leBehrend.threeAPFree_sphere · cited by 1Behrend.threeAPFree_sphereaddRothNumber_lt_of_forall_not_threeAPFree · cited by 0addRothNumber_lt_of_foral…Set · cited by 53352SetAddMonoid · cited by 2864AddMonoidThreeAPFree · cited by 38ThreeAPFreeThreeAPFree.monoCITED BYCITES

Cites3

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
  • AddMonoidstatement and proof · cited by 2,864
  • ThreeAPFreestatement and proof · cited by 38

Cited by5

Results whose statement or proof uses this declaration.