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

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

%proving binary_or_contradiction

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

defaults.assumptions = binary_or_contradiction.conditions

defaults.assumptions:

neither_intro

 ⊢  

neither = neither_intro.instantiate({A:A, B:B})

neither: ,  ⊢  

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

neither.derive_contradiction()

, ,  ⊢  

%qed

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

	step type	requirements	statement
0	generalization	1	⊢
1	instantiation	2, 3, 4	, ,  ⊢
	:
2	theorem		⊢
	proveit.logic.booleans.negation.negation_contradiction
3	assumption		⊢
4	instantiation	5, 6, 7	,  ⊢
	: , :
5	theorem		⊢
	proveit.logic.booleans.disjunction.neither_intro
6	assumption		⊢
7	assumption		⊢