Section KNASTER_TARSKI. (* Reference: "https://www.cs.utexas.edu/users/misra/Notes.dir/KnasterTarski.pdf" written by Jayadev Misra *)
Context {D : Type} {PROSET : isProset D} {COLA : isCola D (PROSET := PROSET)}.

Theorem KnasterTarski_3rd (f : D -> D) (W : ensemble D)
(f_isMonotonic : isMonotonic1 f)
(W_is_a_set_of_fixed_points_of_f : W \subseteq fixedpointsOf f)
: {fix_f : D | is_supremum_in fix_f W (fixedpointsOf f)}.