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

theorem Th23:
  for D be non empty set, G1,G2 be Element of PFuncs(D,REAL) holds
  Sum<*G1,G2*> = G1 + G2
proof
  let D be non empty set, G1,G2 be Element of PFuncs(D,REAL);
  thus Sum<*G1,G2*> = Sum(<*G1*>^<*G2*>) by FINSEQ_1:def 9
    .= Sum<*G1*> + G2 by Th20
    .= G1 + G2 by FINSOP_1:11;
end;
