Theorems · Theorem · combinatorics
SimpleGraph.bot_isContained_iff_card_le
∀ {α : Type u_4} {β : Type u_5} {B : SimpleGraph β} [inst : Fintype α] [inst_1 : Fintype β],
⊥.IsContained B ↔ Fintype.card α ≤ Fintype.card β⊥ is contained in any simple graph having sufficiently many vertices.
- Defined in
- Mathlib.Combinatorics.SimpleGraph.Copy
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Bot.botstatement and proof · cited by 4,720
- SimpleGraphstatement and proof · cited by 3,072
- Fintype.cardstatement and proof · cited by 1,386
- Nonempty.someproof · cited by 340
- SimpleGraph.IsContainedstatement and proof · cited by 68
- SimpleGraph.Copyproof · cited by 49
- Fintype.card_le_of_embeddingproof · cited by 11
- SimpleGraph.Copy.toEmbeddingproof · cited by 9
- Function.Embedding.nonempty_of_card_leproof · cited by 6
- SimpleGraph.Copy.botproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.IsContained.botproof · cited by 0