reserve i,j for Element of NAT,
  x,y,z for FinSequence of COMPLEX,
  c for Element of COMPLEX,
  R,R1,R2 for Element of i-tuples_on COMPLEX;

theorem Th29:
  for x,y being complex-valued FinSequence st len x=len y holds
  -(x + y) = -x + -y
proof
  let x,y be complex-valued FinSequence;
  assume
A1: len x=len y;
A2: len (-y) = len y by Th5; then
A3: len (-x + -y) = len (-x) by A1,Th5,Th6;
A4: len (-x) = len x by Th5;
A5: len (x + y) = len x by A1,Th6;
  then (x + y) + (-x + -y) = y + x + -x + -y by A1,A2,A4,Th24
    .= y + (x + -x) + -y by A1,A4,Th24
    .= y + 0c (len x) + -y by Th28
    .= y + -y by A1,Th27
    .= 0c (len y) by Th28;
  hence thesis by A1,A4,A5,A3,Th26;
end;
