theorem Th36:
  {z} = X \/ Y implies X = {z} & Y = {z} or X = {} & Y = {z} or X
  = {z} & Y = {}
proof
  assume
A1: {z} = X \/ Y;
  X <> {} or Y <> {} by A1;
  hence thesis by A1,Lm3,XBOOLE_1:7;
end;
