If you have a single user in the system, yes, you can have only one proof per standard(requirement now :) )
Think about it :
The proof collection is like this :

_id | user_id | standard_id
---- | --------- | ---------------  
1 | user1 | standard1 |
2 | user2 | standard1 |
3 | user1 | standard2 |

and so on... When you state "Standard has one Proof", you assume you have only one link between the standards and proofs collection, i.e. you cannot have a duplicate standard_id in the proofs collection.