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, ExprRange, ExprTuple, IndexedVar, K, Lambda, V, Variable, n, x
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 And, Equals, Exists, InSet, Set
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda([x_1_to_n], Conditional(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), And(ExprRange(sub_expr1, InSet(IndexedVar(x, sub_expr1), V), one, n)))))

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(x_{1}, x_{2}, \ldots, x_{n}\right) \mapsto \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} \textrm{ if } \left(x_{1} \in V\right) \land  \left(x_{2} \in V\right) \land  \ldots \land  \left(x_{n} \in V\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	parameters: 19 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 30 operands: 5
4	Operation	operator: 32 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	9
7	Operation	operator: 50 operands: 10
8	Operation	operator: 11 operand: 16
9	ExprRange	lambda_map: 13 start_index: 53 end_index: 54
10	ExprTuple	14, 15
11	Literal
12	ExprTuple	16
13	Lambda	parameter: 68 body: 17
14	Operation	operator: 18 operands: 19
15	Operation	operator: 20 operand: 46
16	Lambda	parameters: 21 body: 22
17	Operation	operator: 50 operands: 23
18	Literal
19	ExprTuple	24
20	Literal
21	ExprTuple	25
22	Conditional	value: 26 condition: 27
23	ExprTuple	62, 46
24	ExprRange	lambda_map: 28 start_index: 53 end_index: 54
25	ExprRange	lambda_map: 29 start_index: 53 end_index: 54
26	Operation	operator: 30 operands: 31
27	Operation	operator: 32 operands: 33
28	Lambda	parameter: 68 body: 62
29	Lambda	parameter: 68 body: 63
30	Literal
31	ExprTuple	34, 35
32	Literal
33	ExprTuple	36, 37
34	Operation	operator: 38 operands: 39
35	Operation	operator: 40 operand: 46
36	ExprRange	lambda_map: 42 start_index: 53 end_index: 54
37	Operation	operator: 43 operands: 44
38	Literal
39	ExprTuple	45
40	Literal
41	ExprTuple	46
42	Lambda	parameter: 68 body: 47
43	Literal
44	ExprTuple	48
45	ExprRange	lambda_map: 49 start_index: 53 end_index: 54
46	Variable
47	Operation	operator: 50 operands: 51
48	ExprRange	lambda_map: 52 start_index: 53 end_index: 54
49	Lambda	parameter: 68 body: 55
50	Literal
51	ExprTuple	63, 56
52	Lambda	parameter: 68 body: 57
53	Literal
54	Variable
55	Operation	operator: 58 operands: 59
56	Variable
57	Operation	operator: 60 operands: 61
58	Literal
59	ExprTuple	63, 62
60	Literal
61	ExprTuple	63, 64
62	IndexedVar	variable: 65 index: 68
63	IndexedVar	variable: 66 index: 68
64	Literal
65	Variable
66	Variable
67	ExprTuple	68
68	Variable