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

import proveit
from proveit import defaults
from proveit import A, B, C
from proveit.logic import Implies, Not, Or
theory = proveit.Theory() # the theorem's theory

%proving singular_constructive_dilemma_lemma

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

defaults.assumptions = singular_constructive_dilemma_lemma.conditions

defaults.assumptions:

Implies(A, C).deny_antecedent(assumptions=defaults.assumptions + (Not(C),))

, ,  ⊢  

Implies(B, C).deny_antecedent(assumptions=defaults.assumptions + (Not(C),))

, ,  ⊢  

Or(A, B).affirm_via_contradiction(C)

, , , , ,  ⊢  

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

%qed

proveit.logic.booleans.disjunction.singular_constructive_dilemma_lemma 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	instantiation	12, 10, 11, 15	, ,  ⊢
	: , :
9	instantiation	12, 13, 14, 15	, ,  ⊢
	: , :
10	assumption		⊢
11	assumption		⊢
12	theorem		⊢
	proveit.logic.booleans.implication.modus_tollens_denial
13	assumption		⊢
14	assumption		⊢
15	assumption		⊢