  An Independent Parallelism Theorem is proven in the theory of adhesive HLR
categories. It shows the bijective correspondence between sequential
independent and parallel independent direct derivations in the Weak
Double-Pushout framework, see [2]. The parallel derivations are expressed by
means of Parallel Coherent Transformations (PCTs), hence without assuming the
existence of coproducts compatible with M as in the standard Parallelism
Theorem. It is aslo shown that a derived rule can be extracted from any PCT, in
the sense that to any direct derivation of this rule corresponds a valid PCT.
