notes-rp.md questions/clarification

[yojoe]

I have some questions in understanding the notes-rp.md documentation. Would be great if these questions could be answered or maybe the documentation could be improved.

Here are the following sections:

1. Line 77

bulletproofs/docs/notes-rp.md

Lines 76 to 77 in 1a10ce1

	The statements above are statements about vectors, or equivalently, a
	vector of statements about each entry. We want to combine all of these

The second half of this sentence is confusing: ", a vector of statements about each entry." What is meant by "about each entry"? "entry" of what?

2. Line 80

bulletproofs/docs/notes-rp.md

Line 80 in 1a10ce1

First, we will combine each of the two vector-statements into a single statement.

There are 3 statements in total (lines 62-64) (and all of them are "statements about vectors" as written two sentences before). So which of the 3 statements are meant by each of the two vector-statements? I guess the last two are meant, but the confusing part is that even after the transformation of adding challenger y to statement 2 and 3 there are still 3 statements. How is this supposed to combine statement 2 and 3 into a single one? What's also a bit confusing is that statement 2 and 3 switch position between line 62-64 and 86-88:

bulletproofs/docs/notes-rp.md

Lines 86 to 88 in 1a10ce1

	{\langle {\mathbf{a}}\_{L}, {\mathbf{2}}^{n} \rangle} &= v, \\\\
	{\langle {\mathbf{a}}\_{L} - {\mathbf{1}} - {\mathbf{a}}\_{R}, {\mathbf{y}}^{n} \rangle} &= 0, \\\\
	{\langle {\mathbf{a}}\_{L}, {\mathbf{a}}\_{R} \circ {\mathbf{y}}^{n} \rangle} &= 0

Anyway, after line 88 we still have 3 statements. What have we achieved? Wasn't the idea to get down to 2 statements? And how can adding a random vector "challenger y" combine two statements into one? What's the math/rules behind this?

3. Linex 93 - 101

bulletproofs/docs/notes-rp.md

Lines 93 to 94 in 1a10ce1

	The three resulting statements can then be combined in the same way,
	using the verifier’s choice of \\(z\\):

What is meant by "in the same way"? Previously we added a "challenger vector y" to statement 2 and 3 but still had 3 statements. Now it seems like "challenger scalar z" is added to statement 1 (in square) and to statement 2 but not statement 3 and we add the 3 statements together and end up with one. So it's definitely not "in the same way" and now the 3 statements which were previously separated by a comma are now combined into one statement by plus/addition. It would be helpful to mention the math/rules that allow this transformation. Just a little hint at least for further reading would be great.