reserve G for Graph,
  k, m, n for Nat;

theorem Th3:
  for e being set for s, t being Element of the carrier of G st s =
  (the Source of G).e & t = (the Target of G).e holds <*s, t*> is_vertex_seq_of
  <*e*>
proof
  let e be set;
  let s, t be Element of the carrier of G;
  assume
A1: s = (the Source of G).e & t = (the Target of G).e;
  set c = <*e*>;
  set vs = <*s, t*>;
A2: vs/.(1+1) = t by FINSEQ_4:17;
A3: len c = 1 by FINSEQ_1:39;
  hence len vs = len c + 1 by FINSEQ_1:44;
  let n be Nat;
  assume 1<=n & n<=len c;
  then
A4: n = 1 by A3,XXREAL_0:1;
  c.1 = e & vs/.1 = s by FINSEQ_4:17;
  hence thesis by A1,A4,A2;
end;
