Proof of proveit.logic.sets.inclusion.fold_proper_subset theorem

import proveit
from proveit import A, B
from proveit.logic.sets.inclusion  import proper_subset_def
theory = proveit.Theory() # the theorem's theory

%proving fold_proper_subset

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

# pull in the proper subset definition
proper_subset_def

 ⊢  

proper_subset_def_inst = proper_subset_def.instantiate()

proper_subset_def_inst:  ⊢  

proper_subset_def_inst_derive_left = proper_subset_def_inst.derive_left_via_equality(
        assumptions=[proper_subset_def_inst.rhs])

proper_subset_def_inst_derive_left:  ⊢  

proper_subset_def_inst_derive_left.generalize(
        [[A, B]], conditions=[*proper_subset_def_inst_derive_left.assumptions])

 ⊢  

fold_proper_subset has been proven.  Now simply execute "%qed".

%qed

proveit.logic.sets.inclusion.fold_proper_subset 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.inclusion.proper_subset_def