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 .--> z1) +* (x .--> z2) = f +* (x .--> z2)
proof
A1: dom (x .--> z1) = {x}
    .= dom (x .--> z2);
  thus f +* (x .--> z1) +* (x .--> z2)
   = f +* ((x .--> z1) +* (x .--> z2)) by Th14
    .= f +* (x .--> z2) by A1,Th19;
end;
