Binary Operations Applied to Finite Sequences

For simplicity, we follow the rules: i, j denote natural numbers, F denotes a function from[:D, D′ :] into E, p, q denote finite sequences of elements of D, and p′, q′ denote finite sequences of elements ofD′. Let us consider D, D′, E, F , p, p′. ThenF◦(p, p′) is a finite sequence of elements of E. Let us consider D, D′, E, F , p, d′. ThenF◦(p,d′) is a finite sequence of elements of E. Let us consider D, D′, E, F , d, p′. ThenF◦(d, p′) is a finite sequence of elements of E. Let us consider D, i, d. Theni 7→ d is an element of Di . In the sequelf , f ′ denote functions fromC into D andh denotes a function fromD into E.