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;

theorem Th22:
  i in dom pe & (v=(the Source of G).(pe.i) or v=(the Target of G)
  .(pe.i)) implies v in vertices pe
proof
  set FS=the Source of G, FT=the Target of G;
  assume that
A1: i in dom pe and
A2: v=FS.(pe.i) or v=FT.(pe.i);
  v=FS.(pe/.i) or v=FT.(pe/.i) by A1,A2,PARTFUN1:def 6;
  then v in vertices(pe/.i) by TARSKI:def 2;
  hence thesis by A1;
end;
