Proof of proveit.logic.booleans.fold_is_bool theorem

import proveit
from proveit import defaults
from proveit import A
from proveit.logic import InSet
from proveit.logic.booleans  import bools_def
theory = proveit.Theory() # the theorem's theory

%proving fold_is_bool

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

defaults.assumptions = fold_is_bool.conditions

defaults.assumptions:

bools_def

 ⊢  

A_in_TorF = InSet(A, bools_def.rhs).prove()

A_in_TorF:  ⊢  

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

bools_def.sub_left_side_into(A_in_TorF)

 ⊢  

%qed

proveit.logic.booleans.fold_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, 6, 7, 8	⊢
	: , : , :
4	axiom		⊢
	proveit.logic.booleans.bools_def
5	theorem		⊢
	proveit.logic.sets.enumeration.fold
6	conjecture		⊢
	proveit.numbers.numerals.decimals.nat2
7	instantiation	9	⊢
	: , :
8	assumption		⊢
9	conjecture		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq