Proof of proveit.logic.booleans.implication.contrapose_neg_consequent theorem

import proveit
from proveit import defaults
from proveit.logic import in_bool
from proveit import B
theory = proveit.Theory() # the theorem's theory

%proving contrapose_neg_consequent

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

defaults.assumptions = list(contrapose_neg_consequent.all_conditions()) + [B]

defaults.assumptions:

A_implies_not_b = defaults.assumptions[0]

A_implies_not_b:

A_implies_not_b.deny_antecedent().as_implication(B)

,  ⊢  

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

%qed

proveit.logic.booleans.implication.contrapose_neg_consequent has been proven.

	step type	requirements	statement
0	generalization	1	⊢
1	deduction	2	,  ⊢
2	instantiation	3, 4, 5, 6	, ,  ⊢
	: , :
3	conjecture		⊢
	proveit.logic.booleans.implication.modus_tollens_denial
4	assumption		⊢
5	assumption		⊢
6	instantiation	7, 8	⊢
	:
7	theorem		⊢
	proveit.logic.booleans.negation.double_negation_intro
8	assumption		⊢