reserve a,b,c,d,e,z for object, A,B,C,D,E for set;

theorem
  z in [:A,B,C,D:] implies z = [ z`1_4, z`2_4, z`3_4, z`4_4 ]
proof
  assume
A1: z in [:A,B,C,D:];
  then
A2: C is non empty & D is non empty by MCART_1:51;
  A is non empty & B is non empty by A1,MCART_1:51;
  then ex a being Element of A, b being Element of B, c being Element of C, d
  being Element of D st z = [a,b,c,d] by A1,A2,DOMAIN_1:10;
  hence thesis;
end;

definition
::$CD 5
