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

import proveit
from proveit import defaults
theory = proveit.Theory() # the theorem's theory

%proving set_not_equiv_contradiction

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

defaults.assumptions = set_not_equiv_contradiction.all_conditions()

defaults.assumptions:

A_not_equiv_B = defaults.assumptions[1]

A_not_equiv_B:

not_A_equiv_B = A_not_equiv_B.unfold()

not_A_equiv_B:  ⊢  

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

not_A_equiv_B.derive_contradiction()

,  ⊢  

%qed

proveit.logic.sets.equivalence.set_not_equiv_contradiction has been proven.

	step type	requirements	statement
0	generalization	1	⊢
1	instantiation	2, 3, 4	,  ⊢
	:
2	theorem		⊢
	proveit.logic.booleans.negation.negation_contradiction
3	assumption		⊢
4	instantiation	5, 6	⊢
	: , :
5	theorem		⊢
	proveit.logic.sets.equivalence.unfold_set_not_equiv
6	assumption		⊢