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 ExprTuple, K, V
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, InSet, Set

# build up the expression from sub-expressions
expr = ExprTuple(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())

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\} \in \textrm{LinDepSets}\left(V\right), \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)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

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