theorem :: MATRIX11:48

for n being Nat st n >= 2 holds
ex ODD, EVEN being finite set st
( EVEN = { p where p is Element of Permutations n : p is even } & ODD = { q where q is Element of Permutations n : q is odd } & EVEN /\ ODD = {} & EVEN \/ ODD = Permutations n & card EVEN = card ODD )