theorem Th49:
  for T being finite-branching Tree st not T is finite ex B being
  Branch of T st not B is finite
proof
  let T be finite-branching Tree;
  assume not T is finite;
  then consider C being Chain of T such that
A1: not C is finite by Th48;
  consider B being Branch of T such that
A2: C c= B by TREES_2:28;
  not B is finite by A1,A2;
  hence thesis;
end;
