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

see dependencies

import proveit
from proveit import defaults
from proveit import x, y
from proveit.logic import Equals, TRUE
from proveit.logic.sets.enumeration import singleton_def
%proving in_singleton_eval_true

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

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

defaults.assumptions = in_singleton_eval_true.conditions

defaults.assumptions:

state1 = Equals(Equals(x,y), TRUE).prove()

state1:  ⊢  

state2 = singleton_def.instantiate({x:x, y:y}, auto_simplify=False)

state2:  ⊢  

goal = state2.sub_left_side_into(state1)

goal:  ⊢  

%qed

proveit.logic.sets.enumeration.in_singleton_eval_true 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, 6	⊢
	:
4	instantiation	7	⊢
	: , :
5	axiom		⊢
	proveit.logic.booleans.eq_true_intro
6	assumption		⊢
7	conjecture		⊢
	proveit.logic.sets.enumeration.singleton_def