Mathlib Map

Theorems · Theorem · combinatorics

SimpleGraph.isClique_insert

∀ {α : Type u_1} {G : SimpleGraph α} {s : Set α} {a : α},
  G.IsClique (insert a s) ↔ G.IsClique s ∧ ∀ b ∈ s, a ≠ b → G.Adj a b
Defined in
Mathlib.Combinatorics.SimpleGraph.Clique
Cited by
0 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Set · cited by 53352SetSimpleGraph · cited by 3072SimpleGraphSimpleGraph.Adj · cited by 1346SimpleGraph.AdjSimpleGraph.IsClique · cited by 76SimpleGraph.IsCliqueSet.pairwise_insert_of_symm · cited by 10Set.pairwise_insert_of_sy…SimpleGraph.symm · cited by 8SimpleGraph.symmSimpleGraph.isClique_insertCITED BYCITES

Cites6

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

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.