Proof of proveit.logic.booleans.from_not_false theorem

import proveit
from proveit import defaults
from proveit import A
from proveit.logic.equality import not_equals_contradiction
theory = proveit.Theory() # the theorem's theory

%proving from_not_false

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

defaults.assumptions = from_not_false.conditions

defaults.assumptions:

AneqF = defaults.assumptions[-1]

AneqF:

AneqF.affirm_via_contradiction(A)

,  ⊢  

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

%qed

proveit.logic.booleans.from_not_false has been proven.

	step type	requirements	statement
0	generalization	1	⊢
1	instantiation	2, 3, 4	,  ⊢
	:
2	axiom		⊢
	proveit.logic.booleans.implication.affirmation_via_contradiction
3	assumption		⊢
4	deduction	5	⊢
5	instantiation	6, 7, 8	,  ⊢
	: , :
6	theorem		⊢
	proveit.logic.equality.not_equals_contradiction
7	instantiation	9, 10	⊢
	:
8	assumption		⊢
9	axiom		⊢
	proveit.logic.booleans.negation.negation_elim
10	assumption		⊢