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

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

%proving or_if_only_right

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

defaults.assumptions = or_if_only_right.all_conditions()

defaults.assumptions:

AeqF = A.evaluation()

AeqF:  ⊢  

BeqT = B.evaluation()

BeqT:  ⊢  

false_or_true

 ⊢  

AorT = AeqF.sub_left_side_into(false_or_true, auto_simplify=False)

AorT:  ⊢  

ForT = BeqT.sub_left_side_into(AorT, auto_simplify=False)

ForT: ,  ⊢  

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

%qed

proveit.logic.booleans.disjunction.or_if_only_right has been proven.

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