(*s [(CGconsistent_anchored cg a d)] if there exists a valuation $\rho$ which 
     satisfies [cg] and such that $\rho(a)=d$
*)

Definition CGconsistent_anchored (cg : CGraph1) (a : ad) 
  (d0 : D) := {rho : ad -> D | CGsat cg rho /\ rho a = d0}.

(* Specifications: *)
Lemma CGconsistent_then_anchored : forall cg : CGraph1, CGconsistent cg -> forall (a : ad) (d0 : D), CGconsistent_anchored cg a d0.
Lemma CGanchored_then_consistent : forall (cg : CGraph1) (a : ad) (d0 : D), CGconsistent_anchored cg a d0 -> CGconsistent cg.