Theorems · Theorem · combinatorics
SimpleGraph.Adj.ne
∀ {V : Type u} {G : SimpleGraph V} {a b : V}, G.Adj a b → a ≠ b- Defined in
- Mathlib.Combinatorics.SimpleGraph.Basic
- Cited by
- 39 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Adjstatement and proof · cited by 1,346
- SimpleGraph.ne_of_adjproof · cited by 14
Cited by39
Results whose statement or proof uses this declaration.
- SimpleGraph.edist_eq_one_iff_adjproof · cited by 5
- SimpleGraph.not_isDiag_of_mem_edgeSetproof · cited by 4
- SimpleGraph.deleteEdges_adjproof · cited by 4
- SimpleGraph.IsNClique.insertproof · cited by 3
- SimpleGraph.IsTree.card_edgeFinsetproof · cited by 3
- SimpleGraph.deleteEdges_of_subset_diagSetproof · cited by 3
- SimpleGraph.map_le_iff_le_comapproof · cited by 3
- SimpleGraph.Subgraph.subgraphOfAdj_eq_induceproof · cited by 2
- SimpleGraph.spanningCoe_induce_eq_selfproof · cited by 2
- SimpleGraph.isUniversal_compl_iff_isIsolatedproof · cited by 2
- SimpleGraph.Adj.nontrivialproof · cited by 2
- SimpleGraph.Connected.connected_delete_edge_of_not_isBridgeproof · cited by 2