theorem
  for f be Function, a,b,n,m,x be object st x <> m & x <> a
   holds (f +* (a.--> b) +* (m .--> n)).x=f.x
proof
  let f be Function, a,b,n,m,x be object;
  assume that
A1: x<>m and
A2: x<>a;
  set mn=m .--> n, nm=a .--> b;
A3: not x in dom nm by A2,TARSKI:def 1;
  not x in dom mn by A1,TARSKI:def 1;
  hence (f +* nm +* mn).x=(f +* nm).x by Th11
    .=f.x by A3,Th11;
end;
