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;

theorem Th33:
  f is one-to-one & x in dom f implies x = (f").(f.x) & x = (f"*f) .x
proof
  assume
A1: f is one-to-one;
  assume
A2: x in dom f;
  hence x = (f").(f.x) by A1,Th31;
  hence thesis by A2,Th13;
end;
