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 Th32:
  <*x,y*> is FinTree-yielding iff x is finite Tree & y is finite Tree
proof
A1: x is finite Tree & y is finite Tree iff {x,y} is constituted-FinTrees
  by Th16;
  rng <*x,y*> = {x,y} by FINSEQ_2:127;
  hence thesis by A1;
end;
