
theorem Th21:
  for L being complete LATTICE for S being strict closure System
  of L holds (ClImageMap L)".S = closure_op S
proof
  let L be complete LATTICE;
  let S be infs-inheriting full strict SubRelStr of L;
A1: closure_op S is Element of ClOpers L by Th10;
  (ClImageMap L).closure_op S = Image closure_op S by Def4
    .= S by Th18;
  hence thesis by A1,FUNCT_2:26;
end;
