reserve i,j,n,k for Nat,
  a for Element of COMPLEX,
  R1,R2 for Element of i-tuples_on COMPLEX;

theorem Th8:
  for M being Matrix of COMPLEX holds len (-M)=len M & width (-M)= width M
proof
  let M be Matrix of COMPLEX;
A1: width (-M)=width COMPLEX2Field (-M) by MATRIX_5:7
    .= width COMPLEX2Field Field2COMPLEX (-COMPLEX2Field M) by MATRIX_5:def 4
    .= width (-COMPLEX2Field M) by MATRIX_5:6
    .= width COMPLEX2Field M by MATRIX_3:def 2
    .= width M by MATRIX_5:def 1;
  len (-M)=len COMPLEX2Field (-M) by MATRIX_5:7
    .= len COMPLEX2Field Field2COMPLEX (-COMPLEX2Field M) by MATRIX_5:def 4
    .= len (-COMPLEX2Field M) by MATRIX_5:6
    .= len COMPLEX2Field M by MATRIX_3:def 2
    .= len M by MATRIX_5:def 1;
  hence thesis by A1;
end;
