reserve x,y,z for object, X,Y for set,
  i,k,n for Nat,
  p,q,r,s for FinSequence,
  w for FinSequence of NAT,
  f for Function;

theorem
  for T1,T2 being Tree holds tree(T1,T2)|<*0*> = T1 & tree(T1,T2)|<*1*> = T2
proof
  let T1, T2 be Tree;
  set p = <*T1,T2*>;
A1: len p = 2 by FINSEQ_1:44;
A2: p.1 = T1;
A3: p.2 = T2;
A4: 0+1 = 1;
  1+1 = 2;
  hence thesis by A1,A2,A3,A4,Th49;
end;
