If you have any legal status in Canada, you do not have to prove anything. The PR application will be processed based on your eligibility on what you have claimed.
Also, Canadian immigration allows dual intent.
Dual intent is present when a foreign national who has applied or may apply for permanent residence in Canada also applies to enter Canada for a temporary period as a
Having 2 intents (1 for temporary residence and 1 for permanent residence) is legitimate.
Subsection
A22(2) states: “An intention by a foreign national to become a permanent resident does not preclude them from becoming a temporary resident if the officer is satisfied that they will leave Canada by the end of the period authorized for their stay”. Dual intent on the part of the applicant is therefore not prima facie grounds for refusal of temporary resident status.
Assessing dual intent
A person’s desire to apply for temporary resident status and permanent resident status in Canada is legitimate. An officer should distinguish between a temporary residence applicant whose intentions are bona fide and an applicant who has no intention of leaving Canada at the end of their authorized stay if the application for permanent residence is refused.
In assessing the applicant’s intentions, the individual circumstances of the temporary residence applicant must be examined; refusals of non-bona fide temporary residents may only withstand legal challenge when the refusal is based on the information related to the specific application before an officer.