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 Span, VecSpaces, lin_comb_axn
from proveit.logic import Equals, Forall, InClass, Set, SetOfAll
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(Span(Set(x_1_to_n)), SetOfAll(instance_param_or_params = [a_1_to_n], instance_element = lin_comb_axn, domain = K)).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} \textrm{Span}\left(\left\{x_{1}, x_{2}, \ldots, x_{n}\right\}\right) =  \\ \left\{\left(a_{1} \cdot x_{1}\right) +  \left(a_{2} \cdot x_{2}\right) +  \ldots +  \left(a_{n} \cdot x_{n}\right)\right\}_{a_{1}, a_{2}, \ldots, a_{n} \in K} \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: 48 body: 3
2	ExprTuple	48
3	Conditional	value: 4 condition: 5
4	Operation	operator: 17 operand: 9
5	Operation	operator: 7 operands: 8
6	ExprTuple	9
7	Literal
8	ExprTuple	48, 10
9	Lambda	parameter: 60 body: 12
10	Operation	operator: 13 operand: 69
11	ExprTuple	60
12	Conditional	value: 15 condition: 16
13	Literal
14	ExprTuple	69
15	Operation	operator: 17 operand: 20
16	Operation	operator: 65 operands: 19
17	Literal
18	ExprTuple	20
19	ExprTuple	60, 21
20	Lambda	parameters: 40 body: 22
21	Literal
22	Conditional	value: 23 condition: 24
23	Operation	operator: 25 operands: 26
24	Operation	operator: 53 operands: 27
25	Literal
26	ExprTuple	28, 29
27	ExprTuple	30
28	Operation	operator: 31 operand: 36
29	Operation	operator: 33 operand: 37
30	ExprRange	lambda_map: 35 start_index: 59 end_index: 60
31	Literal
32	ExprTuple	36
33	Literal
34	ExprTuple	37
35	Lambda	parameter: 73 body: 38
36	Operation	operator: 39 operands: 40
37	Lambda	parameters: 41 body: 42
38	Operation	operator: 65 operands: 43
39	Literal
40	ExprTuple	44
41	ExprTuple	45
42	Conditional	value: 46 condition: 47
43	ExprTuple	67, 48
44	ExprRange	lambda_map: 49 start_index: 59 end_index: 60
45	ExprRange	lambda_map: 50 start_index: 59 end_index: 60
46	Operation	operator: 51 operands: 52
47	Operation	operator: 53 operands: 54
48	Variable
49	Lambda	parameter: 73 body: 67
50	Lambda	parameter: 73 body: 68
51	Literal
52	ExprTuple	55
53	Literal
54	ExprTuple	56
55	ExprRange	lambda_map: 57 start_index: 59 end_index: 60
56	ExprRange	lambda_map: 58 start_index: 59 end_index: 60
57	Lambda	parameter: 73 body: 61
58	Lambda	parameter: 73 body: 62
59	Literal
60	Variable
61	Operation	operator: 63 operands: 64
62	Operation	operator: 65 operands: 66
63	Literal
64	ExprTuple	68, 67
65	Literal
66	ExprTuple	68, 69
67	IndexedVar	variable: 70 index: 73
68	IndexedVar	variable: 71 index: 73
69	Variable
70	Variable
71	Variable
72	ExprTuple	73
73	Variable