Proof of proveit.logic.equality.sub_right_side_into theorem

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

%proving sub_right_side_into

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

sub_left_side_into

 ⊢  

sub_left_side_into.instantiate({x:y, y:x}, assumptions=sub_right_side_into.all_conditions())

,  ⊢  

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

%qed

proveit.logic.equality.sub_right_side_into has been proven.

	step type	requirements	statement
0	generalization	1	⊢
1	instantiation	2, 3, 4	,  ⊢
	: , : , :
2	conjecture		⊢
	proveit.logic.equality.sub_left_side_into
3	assumption		⊢
4	instantiation	5, 6	⊢
	: , :
5	conjecture		⊢
	proveit.logic.equality.equals_reversal
6	assumption		⊢