reserve a,x,y for object, A,B for set,
  l,m,n for Nat;

theorem Th30:
  for f be Function, d,i be object st i in dom f holds (f+*(i,d)).i = d
proof
  let f be Function, d,i be object;
A1: i in dom(i.-->d) by TARSKI:def 1;
  assume i in dom f;
  hence (f+*(i,d)).i = (f+*(i.-->d)).i by Def2
    .= (i.-->d).i by A1,FUNCT_4:13
    .= d by FUNCOP_1:72;
end;
