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

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

%proving nand_if_left_but_not_right

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

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

defaults.assumptions = nand_if_left_but_not_right.all_conditions()

defaults.assumptions:

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

AeqT:  ⊢  

BeqF = B.evaluation()

BeqF:  ⊢  

true_and_false_negated

 ⊢  

AnandF = AeqT.sub_left_side_into(true_and_false_negated, auto_simplify=False)

AnandF:  ⊢  

BeqF.sub_left_side_into(AnandF, auto_simplify=False)

,  ⊢  

%qed

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

	step type	requirements	statement
0	generalization	1	⊢
1	instantiation	2, 3, 4	,  ⊢
	: , :
2	theorem		⊢
	proveit.logic.equality.substitute_falsehood
3	instantiation	5, 6, 7	⊢
	: , :
4	assumption		⊢
5	theorem		⊢
	proveit.logic.equality.substitute_truth
6	theorem		⊢
	proveit.logic.booleans.conjunction.true_and_false_negated
7	assumption		⊢