theorem Th23: :: MATRIX11:23

for n being Nat
for K being commutative Ring
for perm2 being Element of Permutations (n + 2) st K is Fanoian & not K is degenerated holds
( ( perm2 is even implies sgn (perm2,K) = 1_ K ) & ( sgn (perm2,K) = 1_ K implies perm2 is even ) & ( perm2 is odd implies sgn (perm2,K) = - (1_ K) ) & ( sgn (perm2,K) = - (1_ K) implies perm2 is odd ) )