Theorems · Theorem · combinatorics
Finset.map_subtype_subset
∀ {α : Type u_1} {t : Set α} (s : Finset ↑t), ↑(Finset.map (Function.Embedding.subtype fun x => x ∈ t) s) ⊆ tIf a Finset of a subtype is converted to the main type with
Embedding.subtype, the result is a subset of the set giving the
subtype.
- Defined in
- Mathlib.Data.Finset.Image
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Set.Elemstatement and proof · cited by 7,166
- Finset.mapstatement and proof · cited by 747
- Function.Embedding.subtypestatement and proof · cited by 128
- Finset.mem_coeproof · cited by 91
- Finset.property_of_mem_map_subtypeproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.isSatisfiable_iff_isFinitelySatisfiableproof · cited by 3
- Finset.subset_set_image_iffproof · cited by 2
- Finset.eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtypeproof · cited by 2
- linearIndepOn_finset_iffₒₛproof · cited by 0
- SimpleGraph.cliqueFree_induce_iffproof · cited by 0