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 Th21:
  vertices(pe^qe) \ X c= V implies vertices(pe) \ X c= V &
  vertices(qe) \ X c= V
proof
A1: rng pe c= rng(pe^qe) & rng qe c= rng(pe^qe) by FINSEQ_1:29,30;
  assume vertices(pe^qe) \ X c= V;
  hence thesis by A1,Th20;
end;
