Expression of type Equals

from the theory of proveit.linear_algebra.tensors

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit.core_expr_types import Q__b_1_to_j, a_1_to_i, b_1_to_j, c_1_to_k, f__b_1_to_j
from proveit.linear_algebra import TensorProd, VecSum
from proveit.linear_algebra.addition import vec_summation_b1toj_fQ
from proveit.logic import Equals

# build up the expression from sub-expressions
expr = Equals(VecSum(index_or_indices = [b_1_to_j], summand = TensorProd(a_1_to_i, f__b_1_to_j, c_1_to_k), condition = Q__b_1_to_j), TensorProd(a_1_to_i, vec_summation_b1toj_fQ, c_1_to_k)).with_wrapping_at(1)

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\begin{array}{c} \begin{array}{l} \left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} f\left(b_{1}, b_{2}, \ldots, b_{j}\right){\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right)\right] \\  = \left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} \left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right]{\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) \end{array} \end{array}

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	(1)	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 10 operand: 7
4	Operation	operator: 14 operands: 6
5	ExprTuple	7
6	ExprTuple	17, 8, 18
7	Lambda	parameters: 27 body: 9
8	Operation	operator: 10 operand: 13
9	Conditional	value: 12 condition: 20
10	Literal
11	ExprTuple	13
12	Operation	operator: 14 operands: 15
13	Lambda	parameters: 27 body: 16
14	Literal
15	ExprTuple	17, 19, 18
16	Conditional	value: 19 condition: 20
17	ExprRange	lambda_map: 21 start_index: 34 end_index: 22
18	ExprRange	lambda_map: 23 start_index: 34 end_index: 24
19	Operation	operator: 25 operands: 27
20	Operation	operator: 26 operands: 27
21	Lambda	parameter: 39 body: 28
22	Variable
23	Lambda	parameter: 39 body: 29
24	Variable
25	Variable
26	Variable
27	ExprTuple	30
28	IndexedVar	variable: 31 index: 39
29	IndexedVar	variable: 32 index: 39
30	ExprRange	lambda_map: 33 start_index: 34 end_index: 35
31	Variable
32	Variable
33	Lambda	parameter: 39 body: 36
34	Literal
35	Variable
36	IndexedVar	variable: 37 index: 39
37	Variable
38	ExprTuple	39
39	Variable