theorem
  Product ((i+j) |->r ) = (Product (i|->r))*(Product (j|->r))
proof
  reconsider i,j as Nat by TARSKI:1;
  reconsider s=r as Element of REAL by XREAL_0:def 1;
  Product ((i+j) |->s) = multreal.(multreal$$(i|->s),multreal$$(j|->s))
  by SETWOP_2:26
    .= (Product (i|->s))*(Product (j|->s)) by BINOP_2:def 11;
  hence thesis;
end;
