Proof of proveit.logic.booleans.conjunction.nand_if_neither theorem

import proveit
from proveit import A, B
from proveit import defaults
from proveit.logic.booleans.conjunction import false_and_false_negated
theory = proveit.Theory() # the theorem's theory

%proving nand_if_neither

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

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

defaults.assumptions = nand_if_neither.all_conditions()

defaults.assumptions:

AeqF = A.evaluation()

AeqF:  ⊢  

BeqF = B.evaluation()

BeqF:  ⊢  

false_and_false_negated

 ⊢  

n_aand_t = AeqF.sub_left_side_into(
    false_and_false_negated.inner_expr().operand.operands[0],
    auto_simplify=False)

n_aand_t:  ⊢  

BeqF.sub_left_side_into(n_aand_t, auto_simplify=False)

,  ⊢  

%qed

proveit.logic.booleans.conjunction.nand_if_neither has been proven.

	step type	requirements	statement
0	generalization	1	⊢
1	instantiation	4, 2, 3	,  ⊢
	: , :
2	instantiation	4, 5, 6	⊢
	: , :
3	assumption		⊢
4	theorem		⊢
	proveit.logic.equality.substitute_falsehood
5	theorem		⊢
	proveit.logic.booleans.conjunction.false_and_false_negated
6	assumption		⊢