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

theorem
  for V being add-associative right_zeroed right_complementable Abelian
  scalar-distributive scalar-associative scalar-unital vector-distributive
  non empty RLSStruct,
  v being Element of V holds
  (- a) * (- v) = a * v
proof
  let V be add-associative right_zeroed right_complementable Abelian
  scalar-distributive scalar-associative scalar-unital vector-distributive
  non empty RLSStruct,
  v be Element of V;
  thus (- a) * (- v) = (- (- a)) * v by Th24
    .= a * v;
end;
