theorem Th12:
  x in dom S`2 implies (v.Val_S(v,S)).x = Val_S(v,S).x
proof
  assume x in dom S`2;
  then
A1: x in dom @S`2 by SUBSTUT1:def 2;
  rng @S`2 c= bound_QC-variables(Al) & dom v = bound_QC-variables(Al)
   by FUNCT_2:def 1;
  then x in dom Val_S(v,S) by A1,RELAT_1:27;
  hence thesis by FUNCT_4:13;
end;
