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`1_4 in A & z`2_4 in B & z`3_4 in C & z`4_4 in D
proof
  assume
A1: z in [:A,B,C,D:];
  then
A2: C is non empty & D is non empty by MCART_1:51;
A3: A is non empty & B is non empty by A1,MCART_1:51;
  then consider
  a being Element of A, b being Element of B, c being Element of C, d
  being Element of D such that
A4: z = [a,b,c,d] by A1,A2,DOMAIN_1:10;
A5: z`3_4 = c & z`4_4 = d by A4;
  z`1_4 = a & z`2_4 = b by A4;
  hence thesis by A3,A2,A5;
end;
