for i, j being Nat st [i,j] in Indices (M @ ) holds
(M @ ) * i,j < 0

proof

let i, j be Nat; :: thesis: ( [i,j] in Indices (M @ ) implies (M @ ) * i,j < 0 )
assume [i,j] in Indices (M @ ) ; :: thesis: (M @ ) * i,j < 0
then A1: [j,i] in Indices M by MATRIX_1:def 7;
then (M @ ) * i,j = M * j,i by MATRIX_1:def 7;
hence (M @ ) * i,j < 0 by A1, Def2; :: thesis: verum

end;

hence M @ is Negative by Def2; :: thesis: verum