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*^C = (A-^B)*^C
proof
A1: now
    assume
A2: not B c= A;
    then
A3: not B*^C c= A*^C or C = {} by Th35;
A4: {}*^C = {} by ORDINAL2:35;
A5: A*^{} = {} by ORDINAL2:38;
    A-^B = {} by A2,Def5;
    hence thesis by A3,A5,A4,Def5,Th56;
  end;
  now
    assume B c= A;
    then A = B+^(A-^B) by Def5;
    then A*^C = B*^C+^(A-^B)*^C by Th46;
    hence thesis by Th52;
  end;
  hence thesis by A1;
end;
