As a rule, we don't use the passive voice with let. In let's get started, the starting point is in view and let's get going, you are on the starting point already. Since this is a mathematically formal usage, i think that.
Let's Dance Wer hat das Finale gewonnen? Wer ist wann ausgeschieden? 1&1
Moreover, there is a sense. Lets is the third person. Thus you don't need to always change each let's/let us with a replacement however we will presume you do, so we could replace let us.
Allow or permit is normally used instead:
We were allowed to do whatever we. I think that let a be a set, let b be a group, and let c be a number. is the most formal phrasing. Let s is the english cohortative word, meaning let us in an exhortation of the group including the speaker to do something.
