Rather than prove that the tenant has broken a long standing rule about not smoking in the property, what you will need to prove, if this matter goes to the eviction hearing stage at the Landlord and Tenant Board, is that the smoking by your tenant is substantially interfering with your reasonable enjoyment.
You would have to document the times and dates that the smoke from the tenant was affecting you. For example, document if the smell of smoke woke you up, or bothered you as you were going to sleep. You could also ask another tenant to be a witness at your hearing to prove your claims.
The first step, however, would be to serve an N5 Notice to Terminate Tenancy for Interfering with Others.
The N5 is a 20-day notice but the tenant has the first 7 days to void the notice by correcting the problems (stop smoking). Otherwise you can file an (L2) application with the Landlord and Tenant Board to go to a hearing and ask for the termination of the tenancy. If you have to go to the Board, it’s very important to bring witnesses to the hearing so if there are any other tenants, you should speak with them and ask them if they would be willing to come to the hearing to testify to what is going on.
There is a very good chance that you will not notice any more smoke for a while after you give the notice. If the notice is voided by the tenant not smoking, you may need to serve a second notice within 6 months if there is a re-occurrence during that time.
The N5 form and instructions are available from the Landlord and Tenant Board website here – https://tribunalsontario.ca/ltb/forms/#landlord-forms
For reference, here is a link to a case involving smoking as a reason to try an evict a tenant: