Proof of proveit.logic.booleans.from_excluded_middle theorem

import proveit
from proveit import defaults
from proveit import A, C
from proveit.logic import in_bool, Implies
from proveit.logic.booleans import unfold_is_bool
theory = proveit.Theory() # the theorem's theory

%proving from_excluded_middle

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

defaults.assumptions = from_excluded_middle.all_conditions()

defaults.assumptions:

unfold_is_bool

 ⊢  

A_or_not_a = unfold_is_bool.instantiate({A:A})

A_or_not_a:  ⊢  

Ctruth = A_or_not_a.derive_via_dilemma(C)

Ctruth: , ,  ⊢  

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

%qed

proveit.logic.booleans.from_excluded_middle has been proven.

	step type	requirements	statement
0	generalization	1	⊢
1	instantiation	2, 9, 3, 4, 5, 6	, ,  ⊢
	: , : , :
2	conjecture		⊢
	proveit.logic.booleans.disjunction.singular_constructive_dilemma
3	instantiation	7, 9	⊢
	:
4	instantiation	8, 9	⊢
	:
5	assumption		⊢
6	assumption		⊢
7	conjecture		⊢
	proveit.logic.booleans.negation.closure
8	conjecture		⊢
	proveit.logic.booleans.unfold_is_bool
9	assumption		⊢