theorem Th42:
  for p2,q2 st q2 = p2" holds sgn(p2,K) = sgn(q2,K)
proof
A1: n+1+1>=0+1 by XREAL_1:6;
  let p2,q2;
  assume q2=p2";
  then
A2: -(1_K,p2)=-(1_K,q2) by A1,MATRIX_7:29;
A3: -(1_K,q2)=sgn(q2,K)*1_K by Th26;
  -(1_K,p2)=sgn(p2,K)*1_K by Th26;
  then sgn(p2,K)*1_K=sgn(q2,K) by A2,A3,VECTSP_1:def 4;
  hence thesis;
end;
