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Theorems · Theorem · combinatorics

SimpleGraph.TripartiteFromTriangles.cliqueFinset_eq_image

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} (t : Finset (α × β × γ)) [inst : DecidableEq α] [inst_1 : DecidableEq β]
  [inst_2 : DecidableEq γ] [inst_3 : Fintype α] [inst_4 : Fintype β] [inst_5 : Fintype γ]
  [SimpleGraph.TripartiteFromTriangles.NoAccidental t],
  (SimpleGraph.TripartiteFromTriangles.graph t).cliqueFinset 3 =
    Finset.image (⇑SimpleGraph.TripartiteFromTriangles.toTriangle) t
Defined in
Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite
Cited by
1 results in Mathlib
Foundations
Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DecidableEqDecidableEqDecidableEqFintypeFintypeFintypeSimpleGraph.TripartiteFromTriangles.NoAccidental
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

SimpleGraph.TripartiteFromTriangles.cliqueFinset_eq_map · cited by 1TripartiteFromTriangles.c…DFunLike.coe · cited by 62936DFunLike.coeFinset · cited by 13712FinsetFintype · cited by 7736FintypeFunction.Embedding · cited by 988Function.EmbeddingFinset.image · cited by 910Finset.imageFinset.coe_image · cited by 222Finset.coe_imageFinset.coe_injective · cited by 127Finset.coe_injectiveSimpleGraph.TripartiteFromTriangles.graph · cited by 27TripartiteFromTriangles.g…SimpleGraph.cliqueFinset · cited by 26SimpleGraph.cliqueFinsetSimpleGraph.TripartiteFromTriangles.toTriangle · cited by 12TripartiteFromTriangles.t…SimpleGraph.TripartiteFromTriangles.NoAccidental · cited by 10TripartiteFromTriangles.N…SimpleGraph.coe_cliqueFinset · cited by 5SimpleGraph.coe_cliqueFin…SimpleGraph.TripartiteFromTriangles.cliqueSet_eq_image · cited by 2TripartiteFromTriangles.c…TripartiteFromTriangles.cliqu…CITED BYCITES

Cites13

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Cited by1

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