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

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

%proving set_equiv_fold

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

defaults.assumptions = set_equiv_fold.conditions

defaults.assumptions:

set_equiv_def

 ⊢  

set_equiv_def.instantiate().derive_left_via_equality()

 ⊢  

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

%qed

proveit.logic.sets.equivalence.set_equiv_fold 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.equivalence.set_equiv_def