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Theorems · Theorem · combinatorics

SimpleGraph.IsNClique.card_eq

∀ {α : Type u_1} {G : SimpleGraph α} {n : ℕ} {s : Finset α}, G.IsNClique n s → s.card = n
Defined in
Mathlib.Combinatorics.SimpleGraph.Clique
Cited by
17 results in Mathlib
Foundations
Depth 13 from the axioms · uses propext
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Around this declaration

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

SimpleGraph.isNClique_iff · cited by 5SimpleGraph.isNClique_iffSimpleGraph.CliqueFree.mono · cited by 4CliqueFree.monoSimpleGraph.IsNClique.insert · cited by 3IsNClique.insertSimpleGraph.IsNClique.erase_of_sup_edge_of_mem · cited by 2IsNClique.erase_of_sup_ed…SimpleGraph.IsNClique.map · cited by 2IsNClique.mapSimpleGraph.CliqueFree.mem_of_sup_edge_isNClique · cited by 2CliqueFree.mem_of_sup_edg…SimpleGraph.IsFiveWheelLike.card_left · cited by 2IsFiveWheelLike.card_leftSimpleGraph.IsNClique.erase_of_mem · cited by 1IsNClique.erase_of_memSimpleGraph.IsFiveWheelLike.not_colorable_succ · cited by 1IsFiveWheelLike.not_color…SimpleGraph.isNClique_map_iff · cited by 1SimpleGraph.isNClique_map…SimpleGraph.is3Clique_iff · cited by 1SimpleGraph.is3Clique_iffSimpleGraph.card_cliqueFinset_le · cited by 1SimpleGraph.card_cliqueFi…SimpleGraph.cliqueNum_induce_le · cited by 0SimpleGraph.cliqueNum_ind…SimpleGraph.cliqueNum_le_chromaticNumber · cited by 0SimpleGraph.cliqueNum_le_…SimpleGraph.cliqueFreeOn_of_card_lt · cited by 0SimpleGraph.cliqueFreeOn_…Finset · cited by 13712FinsetSimpleGraph · cited by 3072SimpleGraphFinset.card · cited by 2327Finset.cardSimpleGraph.IsNClique · cited by 64SimpleGraph.IsNCliqueIsNClique.card_eqCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by17

Results whose statement or proof uses this declaration.