Proof of proveit.logic.equality.equals_reversal theorem

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

%proving equals_reversal

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

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

defaults.assumptions = equals_reversal.all_conditions()

defaults.assumptions:

equals_symmetry

 ⊢  

eq_sym = equals_symmetry.instantiate({x:x, y:y})

eq_sym:  ⊢  

eq_sym.derive_left_via_equality()

 ⊢  

%qed

proveit.logic.equality.equals_reversal has been proven.

	step type	requirements	statement
0	generalization	1	⊢
1	instantiation	2, 3, 4	⊢
	: , :
2	theorem		⊢
	proveit.logic.equality.lhs_via_equality
3	assumption		⊢
4	instantiation	5	⊢
	: , :
5	axiom		⊢
	proveit.logic.equality.equals_symmetry