theorem Th51:
  -p = |[ -p.1,-p.2,-p.3 ]|
proof
    reconsider r = -1 as Element of REAL by XREAL_0:def 1;
    r*p = |[ (-1)*p.1,(-1)*p.2,(-1)*p.3 ]| by Th49
    .= |[ -p.1,-p.2,-p.3 ]|;
    hence thesis;
end;
