Theorems · Theorem · combinatorics
Finset.Colex.toColex_image_lt_toColex_image
∀ {α : Type u_1} {β : Type u_2} [inst : LinearOrder α] [inst_1 : LinearOrder β] {f : α → β} {s t : Finset α},
StrictMono f → (toColex (Finset.image f s) < toColex (Finset.image f t) ↔ toColex s < toColex t)Strictly monotone functions preserve the colex ordering.
- Defined in
- Mathlib.Combinatorics.Colex
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderLinearOrder
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.
- DFunLike.coestatement · cited by 62,936
- Finsetstatement and proof · cited by 13,712
- LinearOrderstatement and proof · cited by 8,572
- Equivstatement · cited by 8,337
- Finset.imagestatement · cited by 910
- StrictMonostatement and proof · cited by 706
- Colexstatement · cited by 131
- toColexstatement · cited by 90
- lt_iff_lt_of_le_iff_leproof · cited by 54
- Finset.Colex.toColex_image_le_toColex_imageproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Finset.kruskal_katona_lovasz_formproof · cited by 1
- Finset.Colex.toColex_image_ofColex_strictMonoproof · cited by 0