reserve i,j,k for Nat;
reserve K for non empty addLoopStr,
  a for Element of K,
  p for FinSequence of the carrier of K,
  R for Element of i-tuples_on the carrier of K;

theorem Th22:
  i in dom -p & a = p.i implies (-p).i = -a
proof
  assume i in dom -p & a = p.i;
  then (-p).i = (comp K).a by FUNCT_1:12;
  hence thesis by VECTSP_1:def 13;
end;
