reserve a,b,p,x,x9,x1,x19,x2,y,y9,y1,y19,y2,z,z9,z1,z2 for object,
   X,X9,Y,Y9,Z,Z9 for set;
reserve A,D,D9 for non empty set;
reserve f,g,h for Function;
reserve A,B for set;
reserve x,y,i,j,k for object;

theorem
  for f being Function, a,b,c being object st a <> c holds (f +* (a .-->b))
  .c = f.c
proof
  let f be Function, a,b,c be object such that
A1: a <> c;
  set g = a .-->b;
  not c in dom g by A1,TARSKI:def 1;
  hence thesis by Th11;
end;
