theorem Th11:
  not x in dom S`2 implies (v.Val_S(v,S)).x = v.x
proof
  assume not x in dom(S`2);
  then
A1: not x in dom @S`2 by SUBSTUT1:def 2;
  dom(@S`2*v) c= dom(@S`2) by RELAT_1:25;
  then not x in dom Val_S(v,S) by A1;
  hence thesis by FUNCT_4:11;
end;
