reserve X,x for set;
reserve k,m,n for Element of NAT,
  p,q,r,s,r9,s9 for Element of HP-WFF,
  T1,T2 for Tree;
reserve T1,T2 for DecoratedTree;

theorem Th8:
  x-tree(T1,T2)|<*0*> = T1 & x-tree(T1,T2)|<*1*> = T2
proof
A1: len<*T1,T2*> = 2 by FINSEQ_1:44;
  thus x-tree(T1,T2)|<*0*> = (x-tree<*T1,T2*>)|<*0*> by TREES_4:def 6
    .= <*T1,T2*>.(0+1) by A1,TREES_4:def 4
    .= T1;
  thus x-tree(T1,T2)|<*1*> = (x-tree<*T1,T2*>)|<*1*> by TREES_4:def 6
    .= <*T1,T2*>.(1+1) by A1,TREES_4:def 4
    .= T2;
end;
