For example, suppose I have a line of a proof introducing new “variable” $x$: $$\textrm{Let}\:\:x\in f(y)$$ I am looking for ways to express the word “let” in this context and I would like to avoid using natural language because Math is itself a universal language for expressing complex ideas.
I used to use a character like a right square bracket or similar to it. I once encountered it somewhere, but I don't know if it is a common practice. For example, I would write that line like this: $$\sqsupset x\in f(y)$$
Now I failed to find this character anywhere, neither on the Web nor in Unicode symbol set. Instead, I discovered some similar symbols like $\buildrel \text{def}\over=$, or $:=$, or $\buildrel\triangle\over=$, or $:\Leftrightarrow$ in Wikipedia, but those are very limited and not so much useful in my case.