theorem Th34:
  for G1,G2 being Subset of S holds G1 c= G2 implies for s being
  Element of S holds s|= Tau(G1,R,BASSIGN) implies s|= Tau(G2,R,BASSIGN)
proof
  let G1,G2 be Subset of S;
  set Tau1 = Tau(G1,R,BASSIGN);
  set Tau2 = Tau(G2,R,BASSIGN);
  assume
A1: G1 c= G2;
  let s be Element of S;
  assume s|= Tau1;
  then (Fid(Tau1,S)).s = TRUE;
  then chi(G1,S).s =1 by Def64;
  then s in G1 by FUNCT_3:def 3;
  then chi(G2,S).s =1 by A1,FUNCT_3:def 3;
  then (Fid(Tau2,S)).s = TRUE by Def64;
  hence thesis;
end;
