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Theorems · Theorem · combinatorics

Finset.card_eq_three

∀ {α : Type u_1} {s : Finset α} [inst : DecidableEq α], s.card = 3 ↔ ∃ x y z, x ≠ y ∧ x ≠ z ∧ y ≠ z ∧ s = {x, y, z}
Defined in
Mathlib.Data.Finset.Card
Cited by
4 results in Mathlib
Foundations
Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DecidableEq
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

SimpleGraph.EdgeDisjointTriangles.card_edgeFinset_le · cited by 1EdgeDisjointTriangles.car…SimpleGraph.egirth_top · cited by 1SimpleGraph.egirth_topSimpleGraph.is3Clique_iff · cited by 1SimpleGraph.is3Clique_iffSimpleGraph.cliqueFree_hasse_three · cited by 0SimpleGraph.cliqueFree_ha…Finset · cited by 13712FinsetFinset.card · cited by 2327Finset.cardFinset.card_eq_succ · cited by 7Finset.card_eq_succFinset.card_eq_threeCITED BYCITES

Cites3

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Cited by4

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