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 A1: i in dom (S | n) ; :: thesis: ex n being Nat st (S | n) . i is Matrix of n,D
take L = len (S . i); :: thesis: (S | n) . i is Matrix of L,D
thus (S | n) . i is Matrix of L,D by A1, FUNCT_1:47; :: thesis: verum

end;

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