Prove it - factorial is bigger than 2^n

I've been doing the scala coursera and wanted to write down the proof that

$factorial(n)\; \ge \; 2$ⁿ when n ≥ 4

since it uses induction and I am out of practise.

Base case

For n = 4

factorial(4) = 4*3*2*1 = 24
and 2⁴ = 2*2*2*2 = 16
and 24 ≥ 16

so $factorial(n)\; \ge \; 2$ⁿ when n = 4

Induction step

For n >= 4 assume we have

$factorial(n)\; >=\; 2$ⁿ

and consider

$factorial(n+1)\; =\; factorial(n)\; \times \; (n+1)$
 ≥ 2ⁿ × (n+1)
 ≥ 2ⁿ × 2 since (n+1) ≥ 2 when n ≥ 4
 = 2ⁿ⁺¹

QED
(I also wanted to learn about writing maths in html)