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 f misses dom h & f c= g +* h implies f c= g
proof assume that
A1: dom f misses dom h and
A2: f c= g +* h;
A3: (g +* h)|dom f = g|dom f +* h|dom f by Th71
      .= g|dom f +* {} by A1,RELAT_1:66
      .= g|dom f;
  f|dom f = f;
  then f c= g|dom f by A2,A3,RELAT_1:76;
 hence f c= g by RELAT_1:184;
end;
