for S being non empty non void ManySortedSign
for s being SortSymbol of S
for X being V5() ManySortedSet of the carrier of S
for x1, x2 being Element of X . s
for T being b₃,b₁ -terms all_vars_including inheriting_operations free_in_itself MSAlgebra over S
for r being Element of T,s holds ((Hom (T,x1,x2)) . s) . r = (((canonical_homomorphism T) ** (Hom ((Free (S,X)),x1,x2))) . s) . r