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, VecZero, lin_comb_axn, some_nonzero_a
from proveit.logic import Equals, Exists, Forall, InSet, Set
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(n, Conditional(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(), InSet(n, NaturalPos))))

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