let n be non empty Element of NAT ; :: thesis: BRoots (unital_poly F_Complex ,n) = (n -roots_of_1 ),1 -bag
set p = unital_poly F_Complex ,n;
A1:
Roots (unital_poly F_Complex ,n) = n -roots_of_1
by Th46;
A2:
support (BRoots (unital_poly F_Complex ,n)) = Roots (unital_poly F_Complex ,n)
by UPROOTS:def 9;
A3: degree (BRoots (unital_poly F_Complex ,n)) =
(len (unital_poly F_Complex ,n)) -' 1
by UPROOTS:61
.=
(n + 1) -' 1
by Th44
.=
n
by NAT_D:34
;
card (n -roots_of_1 ) = n
by Th30;
hence
BRoots (unital_poly F_Complex ,n) = (n -roots_of_1 ),1 -bag
by A1, A2, A3, UPROOTS:15; :: thesis: verum