Sorting Operators for Finite Sequences

(Def. 1)(i) If len f = 0, then maxp f = 0, and (ii) if len f > 0, then maxp f ∈ dom f and for every natural number i and for all real numbers r1, r2 such that i∈ dom f and r1 = f (i) and r2 = f (maxp f ) holds r1 ≤ r2 and for every natural number j such that j ∈ dom f and f ( j) = f (maxp f ) holds maxp f ≤ j. Let f be a finite sequence of elements of R. The functor minp f yields a natural number and is defined by the conditions (Def. 2).