theorem
  for f,g being Assign of BASSModel(R,BASSIGN), X being Subset of S holds
  (TransEU(f,g)).X = SIGMA(g) \/ (SIGMA(f) /\ Pred(X,R))
proof
  let f,g be Assign of BASSModel(R,BASSIGN);
  let X be Subset of S;
  set h = Tau(X,R,BASSIGN);
  (TransEU(f,g)).X = SigFoaxTau(g,f,X,R,BASSIGN) by Def73
    .= SIGMA(g) \/ SIGMA(Fax(f,h)) by Th33
    .= SIGMA(g) \/ (SIGMA(f) /\ SIGMA(EX(h))) by Th33
    .= SIGMA(g) \/ (SIGMA(f) /\ Pred(SIGMA(h),R)) by Th50;
  hence thesis by Th32;
end;
