reserve k,n,m,l,p for Nat;
reserve n0,m0 for non zero Nat;
reserve f for FinSequence;
reserve x,X,Y for set;
reserve f1,f2,f3 for FinSequence of REAL;

theorem Th12:
  f2 = f1 - {0} implies Sum f1 = Sum f2
proof
A1: dom f1 \ f1"{0} c= dom f1 by XBOOLE_1:36;
  assume f2 = f1 - {0};
  hence Sum f1 = Sum f2 by A1,Th11;
end;
