theorem Th9: :: LAPLACE:9

for n being Nat
for K being Fanoian Field
for p2 being Element of Permutations (n + 2)
for i, j being Nat st i in Seg (n + 2) & p2 . i = j holds
ex X being Element of Fin (2Set (Seg (n + 2))) st
( X = { {N,i} where N is Nat : {N,i} in 2Set (Seg (n + 2)) } & the multF of K $$ (X,(Part_sgn (p2,K))) = (power K) . ((- (1_ K)),(i + j)) )