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 Th48:
  W is_weight>=0of G implies cost(pe,W) >= 0
proof
  set f = RealSequence(pe,W);
  assume W is_weight>=0of G;
  then for i be Nat st i in dom f holds f.i >= 0 by Th45;
  hence thesis by RVSUM_1:84;
end;
