reserve x,A,B,X,X9,Y,Y9,Z,V for set;

theorem
  X /\ Y = X \+\ Y \+\ (X \/ Y)
proof
  X \+\ Y = (X \/ Y) \ X /\ Y by Lm5;
  then X \+\ Y c= X \/ Y by Th36;
  then
A1: (X \+\ Y) \ (X \/ Y) = {} by Lm1;
  X \/ Y = (X \+\ Y) \/ X /\ Y by Th93;
  hence thesis by A1,Lm4,Th88;
end;
