Let's say I'm writing a new theorem but I need to introduce concepts, definitions and lemmas, of course valid, in my own way, since I don't know if someone defined them before in the past.
I am concerned that this may be inconvenient in making it public, losing legitimacy in the matter or infringing any copyright.
The answer is a definitive "yes", regarded that these definitions are not a rewording of existing ones or negating known facts. Also, new definitions must be justified and have direct relationship to the subject you present.
This recommendation is from Writing a Research Paper in Mathematics - From an MIT professor
"In the second section of your paper, the introduction, you will begin to lead the reader into your work in particular, zooming in from the big picture towards your specific results. This is the place to introduce the definitions and lemmas which are standard in the field, but which your readers may not know."