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

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

%proving or_if_only_left

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

defaults.assumptions = or_if_only_left.all_conditions()

defaults.assumptions:

AeqT = A.evaluation()

AeqT:  ⊢  

BeqF = B.evaluation()

BeqF:  ⊢  

true_or_false

 ⊢  

AorF = AeqT.sub_left_side_into(true_or_false, auto_simplify=False)

AorF:  ⊢  

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

TorF: ,  ⊢  

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

%qed

proveit.logic.booleans.disjunction.or_if_only_left 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.disjunction.true_or_false
7	assumption		⊢