Expression of type ExprTuple

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 import ExprTuple, Function, V, s
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 ScalarMult, TensorProd, VecSum
from proveit.logic import Equals, Forall, InSet

# build up the expression from sub-expressions
sub_expr1 = [b_1_to_j]
sub_expr2 = Function(s, sub_expr1)
sub_expr3 = ScalarMult(sub_expr2, f__b_1_to_j)
expr = ExprTuple(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(TensorProd(a_1_to_i, sub_expr3, c_1_to_k), V), condition = Q__b_1_to_j), Equals(TensorProd(a_1_to_i, VecSum(index_or_indices = sub_expr1, summand = sub_expr3, condition = Q__b_1_to_j), c_1_to_k), VecSum(index_or_indices = sub_expr1, summand = ScalarMult(sub_expr2, TensorProd(a_1_to_i, f__b_1_to_j, c_1_to_k)), condition = Q__b_1_to_j)).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())

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

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 3 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	8, 9
7	Lambda	parameters: 44 body: 10
8	Operation	operator: 34 operands: 11
9	Operation	operator: 18 operand: 15
10	Conditional	value: 13 condition: 29
11	ExprTuple	37, 14, 39
12	ExprTuple	15
13	Operation	operator: 16 operands: 17
14	Operation	operator: 18 operand: 23
15	Lambda	parameters: 44 body: 20
16	Literal
17	ExprTuple	21, 22
18	Literal
19	ExprTuple	23
20	Conditional	value: 24 condition: 29
21	Operation	operator: 34 operands: 25
22	Variable
23	Lambda	parameters: 44 body: 26
24	Operation	operator: 31 operands: 27
25	ExprTuple	37, 28, 39
26	Conditional	value: 28 condition: 29
27	ExprTuple	36, 30
28	Operation	operator: 31 operands: 32
29	Operation	operator: 33 operands: 44
30	Operation	operator: 34 operands: 35
31	Literal
32	ExprTuple	36, 38
33	Variable
34	Literal
35	ExprTuple	37, 38, 39
36	Operation	operator: 40 operands: 44
37	ExprRange	lambda_map: 41 start_index: 52 end_index: 42
38	Operation	operator: 43 operands: 44
39	ExprRange	lambda_map: 45 start_index: 52 end_index: 46
40	Variable
41	Lambda	parameter: 58 body: 47
42	Variable
43	Variable
44	ExprTuple	48
45	Lambda	parameter: 58 body: 49
46	Variable
47	IndexedVar	variable: 50 index: 58
48	ExprRange	lambda_map: 51 start_index: 52 end_index: 53
49	IndexedVar	variable: 54 index: 58
50	Variable
51	Lambda	parameter: 58 body: 55
52	Literal
53	Variable
54	Variable
55	IndexedVar	variable: 56 index: 58
56	Variable
57	ExprTuple	58
58	Variable