All presented properties are showed by automated theorem-prover Prover9.
(There is no special order in the presentation of the theorems.)

ID	Name	Lemma	Duals
MTA1	right unfold	$1 + x^*\cdot x \leq x^*$	n/a
MTA2	right monoidic unfold	$1 + x^*\cdot (x+1) \leq x^*$	n/a

In general, we write $x,y...$ and $a,b...$ for arbitrary semiring elements and $p,q...$ for tests. If other letters are involved we adapted the original notation of the authors.