User blog comment:Revilo30703/Knuth's Up Arrow Infinite Expantion/@comment-5883141-20160123014850/@comment-27173506-20160123123157

A simple proof by induction that 2^n2=4 where n is an natural number:

1. 2^12=2^2=4

2. 2^n2=2^n-12^n1=2^n-12

3. Repeatedly taking the predecessor of any natural numbr that is not 1 will eventually reduce to one, so 2^n2=2^2=4.