reserve V for non empty RLSStruct;
reserve x,y,y1 for set;
reserve v for VECTOR of V;
reserve a,b for Real;

theorem Th16:
  for V being add-associative right_zeroed right_complementable Abelian
  scalar-distributive scalar-unital vector-distributive non empty RLSStruct,
  v being Element of V holds
  - v = (- 1) * v
proof
  let V be add-associative right_zeroed right_complementable Abelian
  scalar-distributive scalar-unital vector-distributive non empty RLSStruct,
  v be Element of V;
  v + (- 1) * v = 1 * v + (- 1) * v by Def8
    .= (1 + (- 1)) * v by Def6
    .= 0.V by Th10;
  hence (- v) = (- v) + (v + (- 1) * v)
    .= ((- v) + v) + (- 1) * v by Def3
    .= 0.V + (- 1) * v by Def10
    .= (- 1) * v;
end;
