Proof of proveit.logic.sets.membership.fold_not_in_set theorem

see dependencies

import proveit
from proveit import x, S
from proveit.logic.sets.membership  import not_in_set_def
theory = proveit.Theory() # the theorem's theory

%proving fold_not_in_set

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

not_in_set_def

 ⊢  

not_in_set_def_spec = not_in_set_def.instantiate({x:x, S:S})

not_in_set_def_spec:  ⊢  

not_in_set_def_spec.derive_left_via_equality(assumptions=[not_in_set_def_spec.rhs])

 ⊢  

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

%qed

proveit.logic.sets.membership.fold_not_in_set has been proven.

	step type	requirements	statement
0	generalization	1	⊢
1	instantiation	2, 3, 4	⊢
	: , :
2	theorem		⊢
	proveit.logic.equality.lhs_via_equality
3	assumption		⊢
4	instantiation	5	⊢
	: , :
5	axiom		⊢
	proveit.logic.sets.membership.not_in_set_def