reserve x for set,
  D for non empty set,
  k,n,m,i,j,l for Nat,
  K for Field;

theorem Th1:
  for x,y being FinSequence of REAL st len x=len y & x+y=0*(len x)
  holds x=-y & y=-x
proof
  let x,y be FinSequence of REAL;
  assume that
A1: len x=len y and
A2: x + y = 0* (len x);
A3: x = 0* (len x) - y by A1,A2,MATRIXR1:14;
  hence x = -y by A1,MATRIXR1:6;
  thus -x = --y by A1,A3,MATRIXR1:6
    .=y;
end;
