  In this paper, we develop an Isabelle/HOL library of order-theoretic
fixed-point theorems. We keep our formalization as general as possible: we
reprove several well-known results about complete orders, often with only
antisymmetry or attractivity, a mild condition implied by either antisymmetry
or transitivity. In particular, we generalize various theorems ensuring the
existence of a quasi-fixed point of monotone maps over complete relations, and
show that the set of (quasi-)fixed points is itself complete. This result
generalizes and strengthens theorems of Knaster-Tarski, Bourbaki-Witt, Kleene,
Markowsky, Pataraia, Mashburn, Bhatta-George, and Stouti-Maaden.
