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

import proveit
from proveit import defaults
from proveit import C
from proveit.logic import TRUE, Equals
from proveit.logic.booleans.disjunction import singular_constructive_dilemma_lemma
theory = proveit.Theory() # the theorem's theory

%proving singular_constructive_dilemma

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

defaults.assumptions = singular_constructive_dilemma.all_conditions()

defaults.assumptions:

We will use the constrained singular constructive dilemma as a convenient Lemma to prove some $C=\top$ and deriving $C$ from there.

singular_constructive_dilemma_lemma

 ⊢  

singular_constructive_dilemma_lemma.instantiate({C:Equals(C, TRUE)})

, , , ,  ⊢  

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

%qed

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

	step type	requirements	statement
0	generalization	1	⊢
1	instantiation	2, 3	, , , ,  ⊢
	:
2	axiom		⊢
	proveit.logic.booleans.eq_true_elim
3	instantiation	4, 5, 6, 7, 8, 9, 10	, , , ,  ⊢
	: , : , :
4	theorem		⊢
	proveit.logic.booleans.disjunction.singular_constructive_dilemma_lemma
5	assumption		⊢
6	assumption		⊢
7	instantiation	11	⊢
	: , :
8	assumption		⊢
9	deduction	12	⊢
10	deduction	13	⊢
11	axiom		⊢
	proveit.logic.equality.equality_in_bool
12	instantiation	15, 14	,  ⊢
	:
13	instantiation	15, 16	,  ⊢
	:
14	modus ponens	17, 18	,  ⊢
15	axiom		⊢
	proveit.logic.booleans.eq_true_intro
16	modus ponens	19, 20	,  ⊢
17	assumption		⊢
18	assumption		⊢
19	assumption		⊢
20	assumption		⊢