Basic Proofs Collection

e.g. 0
A or not A is a theorem
Proof:
if not ( A or not A ):
	not( A or not A ).  [If-sub]
	if A:
		not( A or not A ). [if-repeat]
		A. [If-sub]
		A or not A. [or-create]
	not A. [contradiction]
	A or not A. [or-create]
not not( A or not A). [not-create]
A or not A. [not-destroy]
!End Proof!

e.g. 1
not A => (A => B) is a theorem
Proof:
If not A:
	If A:
		If not B:
			A.
			not A.
		not not B.
		B.
	A => B.
not A => (A => B).
!End Proof!