Product of Family of Universal Algebras

(Def. 2) lenpr2(h1) = lenh1 and for every n such that n ∈ dompr2(h1) holds pr2(h1)(n) = h1(n)2. Let us consider A, B, let f1 be a homogeneous quasi total non empty partial function from A∗ to A, and let f2 be a homogeneous quasi total non empty partial function from B∗ to B. Let us assume that arity f1 = arity f2. The functor ee f1, f2dd yields a homogeneous quasi total non empty partial function from [:A, B :]∗ to [:A, B :] and is defined by the conditions (Def. 3). (Def. 3)(i) domee f1, f2dd= [:A, B :] f1 , and (ii) for every finite sequence h of elements of [:A, B :] such that h ∈ domee f1, f2dd holds ee f1, f2dd(h) = 〈 f1(pr1(h)), f2(pr2(h))〉. In the sequel h1 denotes a homogeneous quasi total non empty partial function from (the carrier of U1) to the carrier of U1 and h2 denotes a homogeneous quasi total non empty partial function from (the carrier of U2) to the carrier of U2. Let us consider U1, U2. Let us assume that U1 and U2 are similar. The functor Opers(U1,U2) yields a finite sequence of operational functions of [: the carrier of U1, the carrier of U2 :] and is defined by the conditions (Def. 4).