
theorem Th38:
  for T being _Tree for P1, P2 being Path of T st P1.last() = P2
.first() & P1.vertices() /\ P2.vertices() = {P1.last()} holds P1.append(P2) is
  Path-like
proof
  let T be _Tree, P1, P2 be Path of T such that
A1: P1.last() = P2.first() and
A2: P1.vertices() /\ P2.vertices() = {P1.last()};
  per cases;
  suppose
    P1 is trivial;
    hence thesis by A1,Th16;
  end;
  suppose
    P2 is trivial;
    hence thesis by GLIB_001:130;
  end;
  suppose
    P1 is non trivial & P2 is non trivial;
    hence thesis by A1,A2,Th19;
  end;
end;
