
theorem MYF30:
  for k1,k2,k3,k4 being Element of REAL holds
  for Omega being set st Omega={1,2,3,4}
  ex f being Function of Omega,REAL st
   f.1=k1 & f.2=k2 & f.3=k3 & f.4=k4
 proof
  let k1,k2,k3,k4 be Element of REAL;
  let Omega be set;
  assume ASS: Omega={1,2,3,4};
A1: 1 in Omega by ENUMSET1:def 2,ASS;
A2: 2 in Omega by ENUMSET1:def 2,ASS;
A3: 3 in Omega by ENUMSET1:def 2,ASS;
A4: 4 in Omega by ENUMSET1:def 2,ASS;
  reconsider Omega as non empty set by ASS;
   deffunc U(Element of Omega)=Set2_for_RandomVariable(k1,k2,k3,k4,$1);
       consider f being Function of Omega,REAL such that
   B1: for d being Element of Omega holds f.d = U(d) from FUNCT_2:sch 4;
   B2: f.1=k1
   proof
    consider k being Element of Omega such that C1: k=1 by A1;
    f.k=Set2_for_RandomVariable(k1,k2,k3,k4,k) by B1;
    hence thesis by C1, Def77;
   end;
   B3: f.2=k2
   proof
    consider k being Element of Omega such that C1: k=2 by A2;
    f.2=Set2_for_RandomVariable(k1,k2,k3,k4,k) & k=2 by B1, C1;
    then f.2=Set3_for_RandomVariable(k2,k3,k4,k) & k=2 by Def77;
    hence thesis by Def78;
   end;
   B4: f.3=k3
   proof
    consider k being Element of Omega such that C1: k=3 by A3;
    f.k=Set2_for_RandomVariable(k1,k2,k3,k4,k) by B1;
    then f.3=Set3_for_RandomVariable(k2,k3,k4,k) & k=3 by C1,Def77;
    then f.3=Set4_for_RandomVariable(k3,k4,k) & k=3 by Def78;
    hence thesis by Def79;
   end;
   f.4=k4
   proof
    consider k being Element of Omega such that C1: k=4 by A4;
    f.k=Set2_for_RandomVariable(k1,k2,k3,k4,k) by B1;
    then f.4=Set3_for_RandomVariable(k2,k3,k4,k) & k=4 by C1, Def77;
    then f.4=Set4_for_RandomVariable(k3,k4,k) & k=4 by Def78;
    hence thesis by Def79;
   end;
   hence thesis by B2,B3,B4;
 end;
