Proof of proveit.logic.booleans.negation.negation_contradiction theorem

import proveit
from proveit import defaults
from proveit import A
from proveit.logic import Not
from proveit.logic.booleans.negation  import not_t
theory = proveit.Theory() # the theorem's theory

%proving negation_contradiction

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

defaults.assumptions = negation_contradiction.conditions

defaults.assumptions:

AeqT = A.evaluation(assumptions=[A])

AeqT:  ⊢  

not_true = AeqT.sub_right_side_into(Not(A))

not_true: ,  ⊢  

not_t

 ⊢  

not_t.derive_right_via_equality()

,  ⊢  

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

%qed

proveit.logic.booleans.negation.negation_contradiction has been proven.

	step type	requirements	statement
0	generalization	1	⊢
1	instantiation	2, 3, 4	,  ⊢
	: , :
2	theorem		⊢
	proveit.logic.equality.rhs_via_equality
3	instantiation	5, 6, 7	,  ⊢
	: , :
4	axiom		⊢
	proveit.logic.booleans.negation.not_t
5	theorem		⊢
	proveit.logic.equality.substitute_in_true
6	assumption		⊢
7	assumption		⊢