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

theorem Th35:
  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 - b) * v = a * v - b * 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 - b) * v = (a + (- b)) * v .= a * v + (- b) * v by Def6
    .= a * v + b * (- v) by Th24
    .= a * v - b * v by Th25;
end;
