Proof of proveit.logic.sets.equivalence.set_equiv_is_bool theorem

import proveit
from proveit import A, B
from proveit.logic import Boolean, InSet
from proveit.logic.sets.equivalence  import set_equiv_def
theory = proveit.Theory() # the theorem's theory

%proving set_equiv_is_bool

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

set_equiv_def

 ⊢  

set_equiv_def_inst = set_equiv_def.instantiate()

set_equiv_def_inst:  ⊢  

set_equiv_in_bool_as_defined = set_equiv_def_inst.rhs.deduce_in_bool()

set_equiv_in_bool_as_defined:  ⊢  

set_equiv_def_inst.sub_left_side_into(set_equiv_in_bool_as_defined)

 ⊢  

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

%qed

proveit.logic.sets.equivalence.set_equiv_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	⊢
	: , : , :
4	instantiation	7	⊢
	: , :
5	axiom		⊢
	proveit.logic.booleans.quantification.universality.forall_in_bool
6	conjecture		⊢
	proveit.numbers.numerals.decimals.posnat1
7	axiom		⊢
	proveit.logic.sets.equivalence.set_equiv_def