Theorems · Theorem · combinatorics
SimpleGraph.completeMultipartiteGraph.not_cliqueFree_of_le_enatCard
∀ {n : ℕ} {ι : Type u_3} (V : ι → Type u_4) (f : (i : ι) → V i),
↑n ≤ ENat.card ι → ¬(SimpleGraph.completeMultipartiteGraph V).CliqueFree n- Defined in
- Mathlib.Combinatorics.SimpleGraph.Clique
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypeproof · cited by 7,736
- ENatstatement and proof · cited by 4,985
- Infiniteproof · cited by 352
- Nat.cast_leproof · cited by 159
- ENat.cardstatement and proof · cited by 89
- SimpleGraph.CliqueFreestatement · cited by 70
- ENat.card_eq_coe_fintype_cardproof · cited by 15
- SimpleGraph.completeMultipartiteGraphstatement · cited by 11
- fintypeOfNotInfiniteproof · cited by 3
- SimpleGraph.completeMultipartiteGraph.not_cliqueFree_of_le_cardproof · cited by 3
- SimpleGraph.completeMultipartiteGraph.not_cliqueFree_of_infiniteproof · cited by 2
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