now :: thesis: for i being Nat st i in dom (F /^ n) holds
(F /^ n) . i is Matrix of D
let i be Nat; :: thesis: ( i in dom (F /^ n) implies (F /^ n) . i is Matrix of D )
assume A1: i in dom (F /^ n) ; :: thesis: (F /^ n) . i is Matrix of D
i + n in dom F by A1, FINSEQ_5:26;
then F . (n + i) = F /. (n + i) by PARTFUN1:def 6;
hence (F /^ n) . i is Matrix of D by A1, FINSEQ_5:27; :: thesis: verum
end;
hence F /^ n is FinSequence_of_Matrix of D by Def2; :: thesis: verum