let G be Group; :: thesis: for F1, F2 being FinSequence of the carrier of G st G is commutative Group holds
for P being Permutation of (dom F1) st F2 = F1 * P holds
Product F1 = Product F2
let F1, F2 be FinSequence of the carrier of G; :: thesis: ( G is commutative Group implies for P being Permutation of (dom F1) st F2 = F1 * P holds
Product F1 = Product F2 )
set g = the multF of G;
assume G is commutative Group ; :: thesis: for P being Permutation of (dom F1) st F2 = F1 * P holds
Product F1 = Product F2
then the multF of G is commutative by GROUP_3:2;
hence for P being Permutation of (dom F1) st F2 = F1 * P holds
Product F1 = Product F2 by FINSOP_1:7; :: thesis: verum