Proof of proveit.logic.equality.sub_in_left_operands_via_tuple theorem

import proveit
theory = proveit.Theory() # the theorem's theory
from proveit import defaults
from proveit import f, P, x, y
from proveit.core_expr_types.operations  import operands_substitution_via_tuple

%proving sub_in_left_operands_via_tuple

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

defaults.assumptions = sub_in_left_operands_via_tuple.all_conditions()

defaults.assumptions:

operands_substitution_via_tuple

 ⊢  

Px_eq_Py = operands_substitution_via_tuple.instantiate({f:P, y:y}, auto_simplify=False)

Px_eq_Py: ,  ⊢  

Px_eq_Py.derive_left_via_equality()

, ,  ⊢  

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

%qed

proveit.logic.equality.sub_in_left_operands_via_tuple 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, 6, 7	,  ⊢
	: , : , : , :
5	conjecture		⊢
	proveit.core_expr_types.operations.operands_substitution_via_tuple
6	assumption		⊢
7	assumption		⊢