Proof of proveit.logic.sets.enumeration.in_singleton_is_bool theorem

see dependencies

import proveit
from proveit.logic import InSet, Equals, Boolean
from proveit import x, y
from proveit.logic.equality import sub_left_side_into
from proveit.logic.sets.enumeration import singleton_def
%proving in_singleton_is_bool

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

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

state1 = singleton_def.instantiate({x:x, y:y})

state1:  ⊢  

state2 = InSet(Equals(x,y), Boolean).prove()

state2:  ⊢  

state1.sub_left_side_into(state2).generalize([x,y])

 ⊢  

%qed

proveit.logic.sets.enumeration.in_singleton_is_bool has been proven.

	step type	requirements	statement
0	generalization	1	⊢
1	instantiation	2, 3, 4	⊢
	: , : , :
2	theorem		⊢
	proveit.logic.equality.sub_left_side_into
3	instantiation	5	⊢
	: , :
4	instantiation	6	⊢
	: , :
5	axiom		⊢
	proveit.logic.equality.equality_in_bool
6	conjecture		⊢
	proveit.logic.sets.enumeration.singleton_def