reserve X,Y for set, p,x,x1,x2,y,y1,y2,z,z1,z2 for object;
reserve f,g,h for Function;

theorem Th32:
 g c= f implies g = f|dom g
 proof
  assume
A1:  g c= f;
   then dom g c= dom f by RELAT_1:11;
  hence dom g = dom(f|dom g) by RELAT_1:62;
  let x;
  assume
A2: x in dom g;
  hence g.x = f.x by A1,Th2
      .= (f|dom g).x by A2,FUNCT_1:49;
 end;
