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

import proveit
from proveit.logic.sets.equivalence  import set_not_equiv_def
theory = proveit.Theory() # the theorem's theory

%proving set_not_equiv_is_bool

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

set_not_equiv_def

 ⊢  

set_not_equiv_def_inst = set_not_equiv_def.instantiate()

set_not_equiv_def_inst:  ⊢  

negation_in_bool = set_not_equiv_def_inst.rhs.deduce_in_bool()

negation_in_bool:  ⊢  

set_not_equiv_def_inst.sub_left_side_into(negation_in_bool)

 ⊢  

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

%qed

proveit.logic.sets.equivalence.set_not_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	conjecture		⊢
	proveit.logic.booleans.negation.closure
6	instantiation	8	⊢
	: , :
7	axiom		⊢
	proveit.logic.sets.equivalence.set_not_equiv_def
8	conjecture		⊢
	proveit.logic.sets.equivalence.set_equiv_is_bool