reserve X,X1,X2,Y,Y1,Y2 for set, p,x,x1,x2,y,y1,y2,z,z1,z2 for object;
reserve f,g,g1,g2,h for Function,
  R,S for Relation;
reserve e,u for object,
  A for Subset of X;

theorem Th104:
 for g being f-compatible Function holds dom g c= dom f
 proof
  let g be f-compatible Function;
  let x be object;
  assume x in dom g;
   then g.x in f.x by Def14;
  hence x in dom f by Def2;
 end;
