many small grammatical and stylistic changes

grammatical: "Here's" should be "Here are", "rules" is plural.
stylistic: "rules for" is more idiomatic than "rules about".
grammatical: No verb in "One or the other"; changed to "It's one or the other".
code: added implied `fn main() { ... }` because it is referenced in "note: previous borrow ends here"
semantic: "But" seems like the wrong word here, there is now, contrast, only further explanation. "so", "thus" or "therefor" is clearer.
grammatical: Another misuse of "Here's", should be "Here are" (or possibly "Here're").
grammatical: "use" should be capitalized. All other subheadings capitalize the first word.

src/doc/book/references-and-borrowing.md

@@ -179,7 +179,7 @@ As it turns out, there are rules.
 
 # The Rules
 
-Here’s the rules about borrowing in Rust:
+Here are the rules for borrowing in Rust:
 
 First, any borrow must last for a scope no greater than that of the owner.
 Second, you may have one or the other of these two kinds of borrows, but not
@@ -208,12 +208,14 @@ With this in mind, let’s consider our example again.
 Here’s the code:
 
 ```rust,ignore
-let mut x = 5;
-let y = &mut x;
+fn main() {
+    let mut x = 5;
+    let y = &mut x;
 
-*y += 1;
+    *y += 1;
 
-println!("{}", x);
+    println!("{}", x);
+}
 ```
 
 This code gives us this error:
@@ -225,7 +227,7 @@ error: cannot borrow `x` as immutable because it is also borrowed as mutable
 ```
 
 This is because we’ve violated the rules: we have a `&mut T` pointing to `x`,
-and so we aren’t allowed to create any `&T`s. One or the other. The note
+and so we aren’t allowed to create any `&T`s. It's one or the other. The note
 hints at how to think about this problem:
 
 ```text
@@ -243,14 +245,16 @@ In Rust, borrowing is tied to the scope that the borrow is valid for. And our
 scopes look like this:
 
 ```rust,ignore
-let mut x = 5;
+fn main() {
+    let mut x = 5;
 
-let y = &mut x;    // -+ &mut borrow of x starts here
-                   //  |
-*y += 1;           //  |
-                   //  |
-println!("{}", x); // -+ - try to borrow x here
-                   // -+ &mut borrow of x ends here
+    let y = &mut x;    // -+ &mut borrow of x starts here
+                       //  |
+    *y += 1;           //  |
+                       //  |
+    println!("{}", x); // -+ - try to borrow x here
+}                      // -+ &mut borrow of x ends here
+                       
 ```
 
 The scopes conflict: we can’t make an `&x` while `y` is in scope.
@@ -269,12 +273,12 @@ println!("{}", x);  // <- try to borrow x here
 ```
 
 There’s no problem. Our mutable borrow goes out of scope before we create an
-immutable one. But scope is the key to seeing how long a borrow lasts for.
+immutable one. So scope is the key to seeing how long a borrow lasts for.
 
 ## Issues borrowing prevents
 
 Why have these restrictive rules? Well, as we noted, these rules prevent data
-races. What kinds of issues do data races cause? Here’s a few.
+races. What kinds of issues do data races cause? Here are a few.
 
 ### Iterator invalidation
 
@@ -323,7 +327,7 @@ for i in &v {
 
 We can’t modify `v` because it’s borrowed by the loop.
 
-### use after free
+### Use after free
 
 References must not live longer than the resource they refer to. Rust will
 check the scopes of your references to ensure that this is true.