Proof of proveit.logic.booleans.negation.untrue_from_negation theorem

import proveit
from proveit import A
from proveit.logic import Not
from proveit.logic.booleans  import false_not_true
theory = proveit.Theory() # the theorem's theory

%proving untrue_from_negation

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

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

false_not_true

 ⊢  

A_eq_F = Not(A).prove(assumptions=[Not(A)]).equate_negated_to_false()

A_eq_F:  ⊢  

A_untrue = A_eq_F.sub_left_side_into(false_not_true)

A_untrue:  ⊢  

%qed

proveit.logic.booleans.negation.untrue_from_negation has been proven.

	step type	requirements	statement
0	generalization	1	⊢
1	instantiation	2, 3, 4	⊢
	: , :
2	theorem		⊢
	proveit.logic.equality.substitute_falsehood
3	axiom		⊢
	proveit.logic.booleans.false_not_true
4	assumption		⊢