
theorem Th5:
  for D being non empty set, F being (Subset of FinTrees D),
  p being FinSequence of F st len roots p = 1
  ex x being Element of FinTrees D st p = <*x*> & x in F
proof
  let D be non empty set, F be (Subset of FinTrees D), p be FinSequence of F;
  assume len roots p = 1;
  then
A1: dom roots p = Seg 1 by FINSEQ_1:def 3;
A2: dom p = dom roots p by TREES_3:def 18;
  then
A3: 1 in dom p by A1;
  then reconsider x = p.1 as Element of FinTrees D by Th2;
  take x;
  thus thesis by A1,A2,A3,Th2,FINSEQ_1:def 8;
end;
