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;

theorem Th20:
  rng qe c= rng pe & vertices(pe) \ X c= V implies vertices(qe) \ X c= V
proof
  assume that
A1: rng qe c= rng pe and
A2: vertices(pe) \ X c= V;
  vertices qe c= vertices pe by A1,Th19;
  then vertices qe \ X c= vertices(pe) \ X by XBOOLE_1:35;
  hence thesis by A2;
end;
