reserve n,m,i,j,k for Nat,
  x,y,e,X,V,U for set,
  W,f,g for Function;
reserve p,q for FinSequence;
reserve G for Graph,
  pe,qe for FinSequence of the carrier' of G;
reserve v,v1,v2,v3 for Element of G;
reserve p,q for oriented Chain of G;

theorem Th27:
  p is_orientedpath_of v1,v2 implies v1 in vertices p & v2 in vertices p
proof
  assume
A1: p is_orientedpath_of v1,v2;
  then p <> {};
  then 1 <= len p by FINSEQ_1:20;
  then
A2: 1 in dom p & len p in dom p by FINSEQ_3:25;
  (the Source of G).(p.1) = v1 & (the Target of G).(p.(len p))= v2 by A1;
  hence thesis by A2,Th22;
end;
