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

theorem Th12:
  for M1,M2 being Matrix of COMPLEX holds len (M1-M2)=len M1 &
  width (M1-M2)=width M1
proof
  let M1,M2 be Matrix of COMPLEX;
A1: width (M1-M2)=width COMPLEX2Field (M1-M2) by MATRIX_5:7
    .= width COMPLEX2Field Field2COMPLEX ((COMPLEX2Field M1)-(COMPLEX2Field
  M2)) by MATRIX_5:def 5
    .= width ((COMPLEX2Field M1)-(COMPLEX2Field M2)) by MATRIX_5:6
    .= width ((COMPLEX2Field M1)+-(COMPLEX2Field M2)) by MATRIX_4:def 1
    .= width COMPLEX2Field M1 by MATRIX_3:def 3
    .= width M1 by MATRIX_5:def 1;
  len (M1-M2)=len (COMPLEX2Field (M1-M2)) by MATRIX_5:7
    .= len COMPLEX2Field Field2COMPLEX ((COMPLEX2Field M1)-(COMPLEX2Field M2
  )) by MATRIX_5:def 5
    .= len ((COMPLEX2Field M1)-(COMPLEX2Field M2)) by MATRIX_5:6
    .= len ((COMPLEX2Field M1)+-(COMPLEX2Field M2)) by MATRIX_4:def 1
    .= len COMPLEX2Field M1 by MATRIX_3:def 3
    .= len M1 by MATRIX_5:def 1;
  hence thesis by A1;
end;
