diff --git a/bsip-0040.md b/bsip-0040.md
index ccd10d2..17793a6 100644
--- a/bsip-0040.md
+++ b/bsip-0040.md
@@ -103,7 +103,7 @@ List of possible restrictions are:
 | `any`      | [`list`, `of`, `allowed`, `values`] | stateless |
 | `none`     | [`none`, `of`, `these`, `values`] | stateless |
 | `lt, le, gt, ge, eq, neq`      | `comparative` | stateless |
-| `contains, not_contains`      | [`list`, `of`, `values`] | stateless |
+| `contains_all, contains_none`      | [`list`, `of`, `values`] | stateless |
 | `limit` | [`max_cumsum`, `interval_in_sec`]      | [`current_cumsum`, `interval_began`] |
 | `limit_monthly` | [`max_cumsum`, `interval_in_months`]      | [`current_cumsum`, `interval_began`] |
 | `attribute_assert` | list of restrictions | stateless |
@@ -117,15 +117,22 @@ Following cases must hold for a restriction:
 
 Note: 
 - If required a field can be added that stores the assumed type of the argument
+- This list of restrictions may be redefined to improve clarity, performance or to reduce complexity of implementation while maintaining the intended functionality
 
 In the following we list possible `restriction`s. Mentioning `argument value` in the text below refers to the value of 
 the argument of the operation specified by `argument` of a restriction. 
 
 #### `any`
-Stateless assert, all argument types. `Argument value` must be equal to one of values in the data list
+Stateless assert, all argument types. `Argument value` must be equal to one of values in the data list.
+
+Note
+- If beneficial for performance or complexity an additional operator `equal` can be implemented that only compares to one.
 
 #### `none`
-Stateless assert, all argument types. `Argument value` must NOT be equal to any of the values in the list.
+Stateless assert, all argument types. `Argument value` must NOT be equal to any of the values in the list. 
+
+Note
+- If beneficial for performance or complexity an additional operator `not_equal` can be implemented that only compares to one.
 
 #### `lt, le, gt, ge, eq, neq`
 Stateless assert. Allows explicit type conversion:
@@ -140,12 +147,16 @@ The different asserts read as:
 - `gt`: `Argument value` must be greater than `comparative`
 - `ge`: `Argument value` must be greater than or equal to `comparative`
 - `eq`: `Argument value` must equal to `comparative`
-- `eq`: `Argument value` must NOT be equal to `comparative`
+- `neq`: `Argument value` must NOT be equal to `comparative`
 
-#### `contains, not_contains`
+Note
+- `eq` and `neq` are implicit number comparators and not to be mistaken by a strict left must equal right operator, just like `lt, le, gt, ge` (for example, comparing `1 > list object` would have no sense)
+- If beneficial for performance or complexity the implicit type conversions can be removed and distinct operators introduced that do not have implicit type conversions
+
+#### `contains_all, contains_none`
 Stateless assert, for `list` type arguments.
-- `contains`: The `argument value` must contain all items specified by `data`, but can contain more
-- `not_contains`: The `argument value` must NOT contain any of the items specified by `data`, but can contain others
+- `contains_all`: The `argument value` must contain all items specified by `data`, but can contain more
+- `contains_none`: The `argument value` must NOT contain any of the items specified by `data`, but can contain others
 
 #### `limit`
 Stateful assert, only `int` type arguments. When the authority is created, `interval_began` is set to `valid_from` from its custom active authority and `max_cumsum` to `0`. Incoming operations are first tried to match all stateless asserts, 
@@ -375,7 +386,7 @@ the transaction is executed.
 
 We propose do split the implmentation into two milestones. Each milestone will be voted on as a separate BSIP:
 
-1. Implementation of basic functionaliy to allow custom active permissions and authorities, including `any`, `none` and `lt, le, gt, ge, eq, neq`, `contains, not_contains` and `attribute_assert` `asserts`. If deemed necessary by developpers, reduce to only allow one key or one account for every `custom active authority`
+1. Implementation of basic functionaliy to allow custom active permissions and authorities, including `any`, `none` and `lt, le, gt, ge, eq, neq`, `contains_all, contains_none` and `attribute_assert` `asserts`. If deemed necessary by developpers, reduce to only allow one key or one account for every `custom active authority`
 2. Implement stateful asserts `limit` and `limit_monthly`
 3. Implement `logical_or`