Definition name := fin n.Definition name_eq_dec := fin_eq_dec n.Definition nodes := all_fin n.Definition all_names_nodes := all_fin_all n.Definition no_dup_nodes := all_fin_NoDup n.Module FinNameOrderedTypeCompat (N : NatValue) (FN : FinNameType N) <: NameOrderedTypeCompat FN := fin_OT_compat N.Module FinNameOrderedType (N : NatValue) (FN : FinNameType N) <: NameOrderedType FN := fin_OT N.Inductive fin_complete : fin n -> fin n -> Prop :=
  | fin_complete_neq : forall x y, x <> y -> fin_complete x y.Inductive fin_complete : fin n -> fin n -> Prop :=
  | fin_complete_neq : forall x y, x <> y -> fin_complete x y.Definition adjacent_to : relation (fin n) := fin_complete.Definition adjacent_to_dec : forall x y, {adjacent_to x y} + { ~ adjacent_to x y}.

Lemma adjacent_to_irreflexive : Irreflexive adjacent_to.