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 Conditional, ExprTuple, Function, Lambda, Q, f, i, j, k
from proveit.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k
from proveit.logic import And, Equals, Forall, Implies, InSet
from proveit.numbers import Complex, Mult, Natural, NaturalPos, 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([i, j, k], Conditional(Forall(instance_param_or_params = [f, Q], instance_expr = 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)), And(InSet(i, Natural), InSet(j, NaturalPos), InSet(k, Natural)))))

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(i, j, k\right) \mapsto \left\{\forall_{f, Q}~\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) \textrm{ if } i \in \mathbb{N} ,  j \in \mathbb{N}^+ ,  k \in \mathbb{N}\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	69, 80, 73
3	Conditional	value: 4 condition: 5
4	Operation	operator: 24 operand: 8
5	Operation	operator: 37 operands: 7
6	ExprTuple	8
7	ExprTuple	9, 10, 11
8	Lambda	parameters: 12 body: 13
9	Operation	operator: 55 operands: 14
10	Operation	operator: 55 operands: 15
11	Operation	operator: 55 operands: 16
12	ExprTuple	70, 67
13	Operation	operator: 17 operands: 18
14	ExprTuple	69, 20
15	ExprTuple	80, 19
16	ExprTuple	73, 20
17	Literal
18	ExprTuple	21, 22
19	Literal
20	Literal
21	Operation	operator: 24 operand: 26
22	Operation	operator: 24 operand: 27
23	ExprTuple	26
24	Literal
25	ExprTuple	27
26	Lambda	parameters: 71 body: 28
27	Lambda	parameters: 29 body: 30
28	Conditional	value: 31 condition: 63
29	ExprTuple	64, 66
30	Conditional	value: 32 condition: 33
31	Operation	operator: 55 operands: 34
32	Operation	operator: 35 operands: 36
33	Operation	operator: 37 operands: 38
34	ExprTuple	65, 59
35	Literal
36	ExprTuple	39, 40
37	Literal
38	ExprTuple	41, 42
39	Operation	operator: 61 operands: 43
40	Operation	operator: 51 operand: 48
41	ExprRange	lambda_map: 45 start_index: 79 end_index: 69
42	ExprRange	lambda_map: 46 start_index: 79 end_index: 73
43	ExprTuple	64, 47, 66
44	ExprTuple	48
45	Lambda	parameter: 85 body: 49
46	Lambda	parameter: 85 body: 50
47	Operation	operator: 51 operand: 57
48	Lambda	parameters: 71 body: 53
49	Operation	operator: 55 operands: 54
50	Operation	operator: 55 operands: 56
51	Literal
52	ExprTuple	57
53	Conditional	value: 58 condition: 63
54	ExprTuple	74, 59
55	Literal
56	ExprTuple	76, 59
57	Lambda	parameters: 71 body: 60
58	Operation	operator: 61 operands: 62
59	Literal
60	Conditional	value: 65 condition: 63
61	Literal
62	ExprTuple	64, 65, 66
63	Operation	operator: 67 operands: 71
64	ExprRange	lambda_map: 68 start_index: 79 end_index: 69
65	Operation	operator: 70 operands: 71
66	ExprRange	lambda_map: 72 start_index: 79 end_index: 73
67	Variable
68	Lambda	parameter: 85 body: 74
69	Variable
70	Variable
71	ExprTuple	75
72	Lambda	parameter: 85 body: 76
73	Variable
74	IndexedVar	variable: 77 index: 85
75	ExprRange	lambda_map: 78 start_index: 79 end_index: 80
76	IndexedVar	variable: 81 index: 85
77	Variable
78	Lambda	parameter: 85 body: 82
79	Literal
80	Variable
81	Variable
82	IndexedVar	variable: 83 index: 85
83	Variable
84	ExprTuple	85
85	Variable