Expression of type ExprTuple

from the theory of proveit.numbers.multiplication

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, Q, f
from proveit.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Complex, Mult, Sum
from proveit.numbers.summation import summation_b1toj_fQ

# build up the expression from sub-expressions
sub_expr1 = [b_1_to_j]
sub_expr2 = Function(f, sub_expr1)
sub_expr3 = Function(Q, sub_expr1)
expr = ExprTuple(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(sub_expr2, Complex), condition = sub_expr3), Forall(instance_param_or_params = [a_1_to_i, c_1_to_k], instance_expr = Equals(Mult(a_1_to_i, summation_b1toj_fQ, c_1_to_k), Sum(index_or_indices = sub_expr1, summand = Mult(a_1_to_i, sub_expr2, c_1_to_k), condition = sub_expr3)).with_wrapping_at(2), domain = Complex).with_wrapping())

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(f\left(b_{1}, b_{2}, \ldots, b_{j}\right) \in \mathbb{C}\right), \begin{array}{l}\forall_{a_{1}, a_{2}, \ldots, a_{i}, c_{1}, c_{2}, \ldots, c_{k} \in \mathbb{C}}~\\
\left(\begin{array}{c} \begin{array}{l} \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot \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]\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right) =  \\ \left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right)\right] \end{array} \end{array}\right)\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: 4 operand: 6
2	Operation	operator: 4 operand: 7
3	ExprTuple	6
4	Literal
5	ExprTuple	7
6	Lambda	parameters: 51 body: 8
7	Lambda	parameters: 9 body: 10
8	Conditional	value: 11 condition: 43
9	ExprTuple	44, 46
10	Conditional	value: 12 condition: 13
11	Operation	operator: 35 operands: 14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operands: 18
14	ExprTuple	45, 39
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21, 22
19	Operation	operator: 41 operands: 23
20	Operation	operator: 31 operand: 28
21	ExprRange	lambda_map: 25 start_index: 59 end_index: 49
22	ExprRange	lambda_map: 26 start_index: 59 end_index: 53
23	ExprTuple	44, 27, 46
24	ExprTuple	28
25	Lambda	parameter: 65 body: 29
26	Lambda	parameter: 65 body: 30
27	Operation	operator: 31 operand: 37
28	Lambda	parameters: 51 body: 33
29	Operation	operator: 35 operands: 34
30	Operation	operator: 35 operands: 36
31	Literal
32	ExprTuple	37
33	Conditional	value: 38 condition: 43
34	ExprTuple	54, 39
35	Literal
36	ExprTuple	56, 39
37	Lambda	parameters: 51 body: 40
38	Operation	operator: 41 operands: 42
39	Literal
40	Conditional	value: 45 condition: 43
41	Literal
42	ExprTuple	44, 45, 46
43	Operation	operator: 47 operands: 51
44	ExprRange	lambda_map: 48 start_index: 59 end_index: 49
45	Operation	operator: 50 operands: 51
46	ExprRange	lambda_map: 52 start_index: 59 end_index: 53
47	Variable
48	Lambda	parameter: 65 body: 54
49	Variable
50	Variable
51	ExprTuple	55
52	Lambda	parameter: 65 body: 56
53	Variable
54	IndexedVar	variable: 57 index: 65
55	ExprRange	lambda_map: 58 start_index: 59 end_index: 60
56	IndexedVar	variable: 61 index: 65
57	Variable
58	Lambda	parameter: 65 body: 62
59	Literal
60	Variable
61	Variable
62	IndexedVar	variable: 63 index: 65
63	Variable
64	ExprTuple	65
65	Variable