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

import proveit
from proveit import defaults
from proveit import A, B
from proveit.logic import in_bool, Not, Or
from proveit.logic.booleans.implication  import affirm_via_contradiction
theory = proveit.Theory() # the theorem's theory

%proving right_if_not_left

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

defaults.assumptions = [in_bool(A), in_bool(B), Or(A, B), Not(A), Not(B)]

defaults.assumptions:

AorB = Or(A, B)

AorB:

AorB.affirm_via_contradiction(B)

, ,  ⊢  

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

%qed

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

	step type	requirements	statement
0	generalization	1	⊢
1	instantiation	2, 3, 4	, ,  ⊢
	:
2	axiom		⊢
	proveit.logic.booleans.implication.affirmation_via_contradiction
3	assumption		⊢
4	deduction	5	,  ⊢
5	instantiation	6, 7, 8, 9	, ,  ⊢
	: , :
6	theorem		⊢
	proveit.logic.booleans.disjunction.binary_or_contradiction
7	assumption		⊢
8	assumption		⊢
9	assumption		⊢