  We prove the algorithmic canonicity of two classes of $\mu$-inequalities in a
constructive meta-theory of normal lattice expansions. This result
simultaneously generalizes Conradie and Craig's canonicity for
$\mu$-inequalities based on a bi-intuitionistic bi-modal language, and Conradie
and Palmigiano's constructive canonicity for inductive inequalities (restricted
to normal lattice expansions to keep the page limit). Besides the greater
generality, the unification of these strands smoothes the existing treatments
for the canonicity of $\mu$-formulas and inequalities. In particular, the rules
of the algorithm ALBA used for this result have exactly the same formulation as
those of Conradie and Palmigiano, with no additional rule added specifically to
handle the fixed point binders. Rather, fixed points are accounted for by
certain restrictions on the application of the rules, concerning the
order-theoretic properties of the term functions associated with the formulas
to which the rules are applied.
