Proof of proveit.logic.booleans.not_equals_false theorem

import proveit
from proveit import A
from proveit.logic.booleans import true_not_false
theory = proveit.Theory() # the theorem's theory

%proving not_equals_false

With these allowed/disallowed theorem/theory presumptions (e.g., to avoid circular dependencies), we begin our proof of
not_equals_false:
(see dependencies)

not_equals_false may now be readily provable (assuming required theorems are usable).  Simply execute "%qed".

true_not_false

 ⊢  

AeqT = A.evaluation(assumptions=[A])

AeqT:  ⊢  

AeqT.sub_left_side_into(true_not_false)

 ⊢  

%qed

proveit.logic.booleans.not_equals_false has been proven.

	step type	requirements	statement
0	generalization	1	⊢
1	instantiation	2, 3, 4	⊢
	: , :
2	theorem		⊢
	proveit.logic.equality.substitute_truth
3	theorem		⊢
	proveit.logic.booleans.true_not_false
4	assumption		⊢