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
  dom g misses dom h implies f +* g +* h +* g = f +* g +* h
 proof assume
A1: dom g misses dom h;
  thus f +* g +* h +* g
     = f +* (g +* h) +* g by Th14
    .= f +* (g +* h +* g) by Th14
    .= f +* (h +* g +* g) by A1,Th35
    .= f +* (h +* g)
    .= f +* (g +* h) by A1,Th35
    .= f +* g +* h by Th14;
 end;
