  Matrix properties are a type of property of categories which includes the
ones of being Mal'tsev, arithmetical, majority, unital, strongly unital and
subtractive. Recently, an algorithm has been developed to determine
implications $M\Rightarrow N$ between them. We show here that this algorithm
reduces to construct a partial term corresponding to $N$ from a partial term
corresponding to $M$. Moreover, we prove that this is further equivalent to the
corresponding implication between the weak versions of these properties, i.e.,
the one where only strong monomorphisms are considered instead of all
monomorphisms.
