One year ago, I started working on a subject with one of the professors of our department. The idea was mine, and all of the subsequent steps including modellings, simulations, generation of figures, writing the paper and even responding to the reviewers were done by myself completely, and the professor just reviewed the paper and reminded some typos and minor mistakes of this kind, and also added a short paragraph (completely unnecessary in my opinion) to the Introduction section.
But at the end he wrote his name as the first author and submitted the paper. He told me that being second author for him means getting no credit from the department.
Anyway, I'm going to apply for grad school, and he told me he will compensate in the recommendation he will write for me.
As this is my only published paper as an undergrad, and being first author means everything for me in my application, is there any way for me to prove to the admission committees (or the professors; whoever will review my application) that I was the main contributor of the paper?