S /^ n is Square-Matrix-yielding

proof

let i be Nat; :: according to MATRIXJ1:def 6 :: thesis: ( i in dom (S /^ n) implies ex n being Nat st (S /^ n) . i is Matrix of n,D )
assume A2: i in dom (S /^ n) ; :: thesis: ex n being Nat st (S /^ n) . i is Matrix of n,D
i + n in dom S by A2, FINSEQ_5:26;
then A3: S . (n + i) = S /. (n + i) by PARTFUN1:def 6;
take L = len (S . (n + i)); :: thesis: (S /^ n) . i is Matrix of L,D
(S /^ n) . i = (S /^ n) /. i by A2, PARTFUN1:def 6;
hence (S /^ n) . i is Matrix of L,D by A2, A3, FINSEQ_5:27; :: thesis: verum

end;

hence S /^ n is FinSequence_of_Square-Matrix of D ; :: thesis: verum