Theorems · Theorem · combinatorics
SimpleGraph.induce_eq_top
∀ {α : Type u_1} {G : SimpleGraph α} {s : Set α}, SimpleGraph.induce s G = ⊤ ↔ G.IsClique s- Defined in
- Mathlib.Combinatorics.SimpleGraph.Clique
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Top.topstatement and proof · cited by 9,680
- Set.Elemstatement and proof · cited by 7,166
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Adjproof · cited by 1,346
- Set.Pairwiseproof · cited by 321
- SimpleGraph.inducestatement and proof · cited by 80
- SimpleGraph.IsCliquestatement · cited by 76
- SimpleGraph.extproof · cited by 59
- SimpleGraph.Adj.neproof · cited by 39
- SimpleGraph.isClique_iffproof · cited by 3
- SimpleGraph.induce_adjproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.isClique_iff_induce_eqproof · cited by 0