reserve n,m for Nat,
  r,r1,r2,s,t for Real,
  x,y for set;

theorem
  for D be non empty set, F be PartFunc of D,REAL, X,Y be set st dom(F|(
  X \/ Y)) is finite & X misses Y holds Sum(F, X \/ Y) = Sum(F,X) + Sum (F,Y)
proof
  let D be non empty set, F be PartFunc of D,REAL, X,Y be set;
  assume dom(F|(X \/ Y)) is finite & X misses Y;
  hence Sum(F, X \/ Y) = Sum (FinS(F,X) ^ FinS(F,Y)) by Th76,RFINSEQ:9
    .= Sum(F,X) + Sum(F,Y) by RVSUM_1:75;
end;
