(*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.