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 Th33:
  for x,y,z being complex-valued FinSequence st
  len x=len y & len y=len z holds x - (y - z) = x - y + z
proof
  let x,y,z be complex-valued FinSequence;
  assume that
A1: len x=len y and
A2: len y=len z;
A3: len (-y) = len y by Th5;
  x - (y - z) = x + (- y + z) by A2,Th32
    .= x - y + z by A1,A2,A3,Th24;
  hence thesis;
end;
