Proof of proveit.logic.equality.fold_not_equals theorem

import proveit
from proveit import defaults
from proveit import x, y
from proveit.logic.equality  import not_equals_def
theory = proveit.Theory() # the theorem's theory

%proving fold_not_equals

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

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

defaults.assumptions = fold_not_equals.conditions

defaults.assumptions:

not_equals_def

 ⊢  

not_equals_def.instantiate({x:x, y:y}).derive_left_via_equality()

 ⊢  

%qed

proveit.logic.equality.fold_not_equals has been proven.

	step type	requirements	statement
0	generalization	1	⊢
1	instantiation	2, 3	⊢
	:
2	axiom		⊢
	proveit.logic.booleans.eq_true_elim
3	instantiation	4, 5*	⊢
	: , :
4	axiom		⊢
	proveit.logic.equality.not_equals_def
5	instantiation	6, 7	⊢
	:
6	axiom		⊢
	proveit.logic.booleans.eq_true_intro
7	assumption		⊢
*equality replacement requirements