reserve x,y,x1,x2,z for set,
  n,m,k for Nat,
  t1 for (DecoratedTree of [: NAT,NAT :]),
  w,s,t,u for FinSequence of NAT,
  D for non empty set;
reserve s9,w9,v9 for Element of NAT*;
reserve p,q for MP-variable;
reserve A,A1,B,B1,C,C1 for MP-wff;

theorem Th27:
  @p = @q implies p = q
proof
  assume
A1: @p = @q;
A2: {} in elementary_tree 0 by TREES_1:22;
  then p = @p.{} by FUNCOP_1:7
    .= q by A2,A1,FUNCOP_1:7;
  hence thesis;
end;
