Proof of proveit.logic.booleans.disjunction.neither_intro theorem

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

%proving neither_intro

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

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

defaults.assumptions = neither_intro.all_conditions()

defaults.assumptions:

AeqF = A.evaluation()

AeqF:  ⊢  

BeqF = B.evaluation()

BeqF:  ⊢  

false_or_false_negated

 ⊢  

AorF = AeqF.sub_left_side_into(false_or_false_negated.inner_expr().operand.operands[0],
                               auto_simplify=False)

AorF:  ⊢  

ForF = BeqF.sub_left_side_into(AorF, auto_simplify=False)

ForF: ,  ⊢  

%qed

proveit.logic.booleans.disjunction.neither_intro 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.disjunction.false_or_false_negated
6	assumption		⊢