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

theorem Th48:
  for D be non empty set, F be PartFunc of D,REAL holds F - 0 = F
proof
  let D be non empty set, F be PartFunc of D,REAL;
A1: now
    let d be Element of D;
    assume d in dom F;
    hence (F - 0).d = F.d - 0 by VALUED_1:3
      .= F.d;
  end;
  dom(F - 0) = dom F by VALUED_1:3;
  hence thesis by A1,PARTFUN1:5;
end;
