The idea is correct, but there are several small flaws.

Rather, P(1) is true where P(n) is " is divisible by 6."

Should be: "Show that P(k + 1) is true."

By 6.

(7 - 4) should be (4 - 7).

What exactly does => mean here? Especially, what is the relationship between and ?

Assuming n = k, the fact that n = k + 1 is obviously false.

Edit: Added remark about 4 - 7.