Expression of type ExprTuple

from the theory of proveit.linear_algebra.vector_sets

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, K, Lambda, V, n
from proveit.core_expr_types import a_1_to_n, x_1_to_n
from proveit.linear_algebra import LinDepSets, VecSpaces, VecZero, lin_comb_axn, some_nonzero_a
from proveit.logic import Equals, Exists, Forall, InClass, InSet, Set
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(V, Conditional(Forall(instance_param_or_params = [n], instance_expr = Forall(instance_param_or_params = [x_1_to_n], instance_expr = Equals(InSet(Set(x_1_to_n), LinDepSets(V)), Exists(instance_param_or_params = [a_1_to_n], instance_expr = Equals(lin_comb_axn, VecZero(V)), domain = K, condition = some_nonzero_a).with_wrapping()).with_wrapping_at(2), domain = V).with_wrapping(), domain = NaturalPos), InClass(V, VecSpaces(K)))))

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(V \mapsto \left\{\forall_{n \in \mathbb{N}^+}~\left[\begin{array}{l}\forall_{x_{1}, x_{2}, \ldots, x_{n} \in V}~\\
\left(\begin{array}{c} \begin{array}{l} \left(\left\{x_{1}, x_{2}, \ldots, x_{n}\right\} \in \textrm{LinDepSets}\left(V\right)\right) =  \\ \left[\begin{array}{l}\exists_{a_{1}, a_{2}, \ldots, a_{n} \in K~|~\left(a_{1} \neq 0\right) \lor  \left(a_{2} \neq 0\right) \lor  \ldots \lor  \left(a_{n} \neq 0\right)}~\\
\left(\left(\left(a_{1} \cdot x_{1}\right) +  \left(a_{2} \cdot x_{2}\right) +  \ldots +  \left(a_{n} \cdot x_{n}\right)\right) = \vec{0}\left(V\right)\right)\end{array}\right] \end{array} \end{array}\right)\end{array}\right] \textrm{ if } V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\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	parameter: 65 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 16 operand: 8
4	Operation	operator: 6 operands: 7
5	ExprTuple	8
6	Literal
7	ExprTuple	65, 9
8	Lambda	parameter: 73 body: 11
9	Operation	operator: 12 operand: 75
10	ExprTuple	73
11	Conditional	value: 14 condition: 15
12	Literal
13	ExprTuple	75
14	Operation	operator: 16 operand: 19
15	Operation	operator: 69 operands: 18
16	Literal
17	ExprTuple	19
18	ExprTuple	73, 20
19	Lambda	parameters: 38 body: 21
20	Literal
21	Conditional	value: 22 condition: 23
22	Operation	operator: 49 operands: 24
23	Operation	operator: 51 operands: 25
24	ExprTuple	26, 27
25	ExprTuple	28
26	Operation	operator: 69 operands: 29
27	Operation	operator: 30 operand: 35
28	ExprRange	lambda_map: 32 start_index: 72 end_index: 73
29	ExprTuple	33, 34
30	Literal
31	ExprTuple	35
32	Lambda	parameter: 87 body: 36
33	Operation	operator: 37 operands: 38
34	Operation	operator: 39 operand: 65
35	Lambda	parameters: 40 body: 41
36	Operation	operator: 69 operands: 42
37	Literal
38	ExprTuple	43
39	Literal
40	ExprTuple	44
41	Conditional	value: 45 condition: 46
42	ExprTuple	81, 65
43	ExprRange	lambda_map: 47 start_index: 72 end_index: 73
44	ExprRange	lambda_map: 48 start_index: 72 end_index: 73
45	Operation	operator: 49 operands: 50
46	Operation	operator: 51 operands: 52
47	Lambda	parameter: 87 body: 81
48	Lambda	parameter: 87 body: 82
49	Literal
50	ExprTuple	53, 54
51	Literal
52	ExprTuple	55, 56
53	Operation	operator: 57 operands: 58
54	Operation	operator: 59 operand: 65
55	ExprRange	lambda_map: 61 start_index: 72 end_index: 73
56	Operation	operator: 62 operands: 63
57	Literal
58	ExprTuple	64
59	Literal
60	ExprTuple	65
61	Lambda	parameter: 87 body: 66
62	Literal
63	ExprTuple	67
64	ExprRange	lambda_map: 68 start_index: 72 end_index: 73
65	Variable
66	Operation	operator: 69 operands: 70
67	ExprRange	lambda_map: 71 start_index: 72 end_index: 73
68	Lambda	parameter: 87 body: 74
69	Literal
70	ExprTuple	82, 75
71	Lambda	parameter: 87 body: 76
72	Literal
73	Variable
74	Operation	operator: 77 operands: 78
75	Variable
76	Operation	operator: 79 operands: 80
77	Literal
78	ExprTuple	82, 81
79	Literal
80	ExprTuple	82, 83
81	IndexedVar	variable: 84 index: 87
82	IndexedVar	variable: 85 index: 87
83	Literal
84	Variable
85	Variable
86	ExprTuple	87
87	Variable