reserve fi,psi for Ordinal-Sequence,
  A,A1,B,C,D for Ordinal,
  X,Y for set,
  x,y for object;

theorem
  A c= B implies C-^B c= C-^A
proof
  assume
A1: A c= B;
  then
A2: B = A+^(B-^A) by Def5;
A3: now
    assume
A4: B c= C;
    then
A5: C = B+^(C-^B) by Def5;
    A c= C by A1,A4;
    then B+^(C-^B) = A+^(C-^A) by A5,Def5;
    then A+^((B-^A)+^(C-^B)) = A+^(C-^A) by A2,Th30;
    then (B-^A)+^(C-^B) = C-^A by Th21;
    hence thesis by Th24;
  end;
  not B c= C implies thesis by Def5;
  hence thesis by A3;
end;
