
theorem
  for n being Nat, P1, P2 being n-edge Path-like _Graph
  holds P2 is P1-isomorphic
proof
  let n be Nat, P1, P2 be n-edge Path-like _Graph;
  P1.size() = n & P2.size() = n by GLIB_013:def 4;
  then P1.order() = n + 1 & P2.order() = n + 1 by GLIB_002:46;
  then P1 is (n+1)-vertex & P2 is (n+1)-vertex by GLIB_013:def 3;
  hence thesis by Th32;
end;
