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

see dependencies

import proveit
from proveit import n, x, y
from proveit.numbers import one
from proveit.numbers.numerals.decimals import nat1
from proveit.logic.booleans.disjunction import unary_or_reduction
from proveit.logic.sets.enumeration  import enum_set_def

%proving singleton_def

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

enum_set_def

 ⊢  

enum_set_def.instantiate({n:one, x:x, y:[y]})

 ⊢  

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

%qed

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

	step type	requirements	statement
0	generalization	1	⊢
1	instantiation	2, 3, 4*	⊢
	: , : , :
2	axiom		⊢
	proveit.logic.sets.enumeration.enum_set_def
3	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
4	instantiation	5, 6	⊢
	:
5	conjecture		⊢
	proveit.logic.booleans.disjunction.unary_or_reduction
6	instantiation	7	⊢
	: , :
7	axiom		⊢
	proveit.logic.equality.equality_in_bool
*equality replacement requirements