{M : Type u} →
  {P : Sort u_1} →
    {toAddLeftCancelMonoid : AddLeftCancelMonoid M} →
      {toIsRightCancelAdd : IsRightCancelAdd M} →
        {toAddLeftCancelMonoid' : AddLeftCancelMonoid M} →
          {toIsRightCancelAdd' : IsRightCancelAdd M} →
            { toAddLeftCancelMonoid := toAddLeftCancelMonoid, toIsRightCancelAdd := toIsRightCancelAdd } =
                { toAddLeftCancelMonoid := toAddLeftCancelMonoid', toIsRightCancelAdd := toIsRightCancelAdd' } →
              (toAddLeftCancelMonoid ≍ toAddLeftCancelMonoid' → P) → P