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;
reserve x for set;
reserve x for object;

theorem
  (f +* (x .-->y)).x = y
proof
A1: x in {x} by TARSKI:def 1;
  then dom(x .--> y) = {x} & x in dom f \/ {x} by XBOOLE_0:def 3;
 hence (f +* (x .-->y) ).x = (x .-->y).x by A1,Def1
    .= y by FUNCOP_1:72;
end;
