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, Lambda, 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, Implies, 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(Lambda([f, Q], Implies(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()).with_wrapping_at(2)))

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(\left(f, Q\right) \mapsto \left(\begin{array}{c} \begin{array}{l} \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)\right] \Rightarrow  \\ \left[\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] \end{array} \end{array}\right)\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	55, 52
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 9 operand: 11
7	Operation	operator: 9 operand: 12
8	ExprTuple	11
9	Literal
10	ExprTuple	12
11	Lambda	parameters: 56 body: 13
12	Lambda	parameters: 14 body: 15
13	Conditional	value: 16 condition: 48
14	ExprTuple	49, 51
15	Conditional	value: 17 condition: 18
16	Operation	operator: 40 operands: 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	ExprTuple	50, 44
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	26, 27
24	Operation	operator: 46 operands: 28
25	Operation	operator: 36 operand: 33
26	ExprRange	lambda_map: 30 start_index: 64 end_index: 54
27	ExprRange	lambda_map: 31 start_index: 64 end_index: 58
28	ExprTuple	49, 32, 51
29	ExprTuple	33
30	Lambda	parameter: 70 body: 34
31	Lambda	parameter: 70 body: 35
32	Operation	operator: 36 operand: 42
33	Lambda	parameters: 56 body: 38
34	Operation	operator: 40 operands: 39
35	Operation	operator: 40 operands: 41
36	Literal
37	ExprTuple	42
38	Conditional	value: 43 condition: 48
39	ExprTuple	59, 44
40	Literal
41	ExprTuple	61, 44
42	Lambda	parameters: 56 body: 45
43	Operation	operator: 46 operands: 47
44	Literal
45	Conditional	value: 50 condition: 48
46	Literal
47	ExprTuple	49, 50, 51
48	Operation	operator: 52 operands: 56
49	ExprRange	lambda_map: 53 start_index: 64 end_index: 54
50	Operation	operator: 55 operands: 56
51	ExprRange	lambda_map: 57 start_index: 64 end_index: 58
52	Variable
53	Lambda	parameter: 70 body: 59
54	Variable
55	Variable
56	ExprTuple	60
57	Lambda	parameter: 70 body: 61
58	Variable
59	IndexedVar	variable: 62 index: 70
60	ExprRange	lambda_map: 63 start_index: 64 end_index: 65
61	IndexedVar	variable: 66 index: 70
62	Variable
63	Lambda	parameter: 70 body: 67
64	Literal
65	Variable
66	Variable
67	IndexedVar	variable: 68 index: 70
68	Variable
69	ExprTuple	70
70	Variable