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

theorem Th14:
  for D be non empty set holds addpfunc(D) is commutative
proof
  let D be non empty set;
  let F1,F2 be Element of PFuncs(D,REAL);
  set o=addpfunc(D);
  thus o.(F1,F2) = F2+F1 by Def4
    .= o.(F2,F1) by Def4;
end;
