Proof of proveit.logic.equality.not_equals_contradiction theorem

import proveit
from proveit import defaults
from proveit.logic.equality  import not_equals_def
from proveit.logic.equality import not_equals_contradiction, unfold_not_equals
from proveit.logic.booleans.negation import negation_contradiction
theory = proveit.Theory() # the theorem's theory

%proving not_equals_contradiction

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

defaults.assumptions = not_equals_contradiction.conditions

defaults.assumptions:

x_neq_y = defaults.assumptions[1]

x_neq_y:

not__x_eq_y = x_neq_y.unfold()

not__x_eq_y:  ⊢  

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

not__x_eq_y.derive_contradiction()

,  ⊢  

%qed

proveit.logic.equality.not_equals_contradiction has been proven.

	step type	requirements	statement
0	generalization	1	⊢
1	instantiation	2, 3, 4	,  ⊢
	:
2	conjecture		⊢
	proveit.logic.booleans.negation.negation_contradiction
3	assumption		⊢
4	instantiation	5, 6	⊢
	: , :
5	conjecture		⊢
	proveit.logic.equality.unfold_not_equals
6	assumption		⊢