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, 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, Set, SetOfAll
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(K, Forall(instance_param_or_params = [V], instance_expr = 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), domain = 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(K \mapsto \left[\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\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]\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: 72 body: 2
2	Operation	operator: 20 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 51 body: 6
5	ExprTuple	51
6	Conditional	value: 7 condition: 8
7	Operation	operator: 20 operand: 12
8	Operation	operator: 10 operands: 11
9	ExprTuple	12
10	Literal
11	ExprTuple	51, 13
12	Lambda	parameter: 63 body: 15
13	Operation	operator: 16 operand: 72
14	ExprTuple	63
15	Conditional	value: 18 condition: 19
16	Literal
17	ExprTuple	72
18	Operation	operator: 20 operand: 23
19	Operation	operator: 68 operands: 22
20	Literal
21	ExprTuple	23
22	ExprTuple	63, 24
23	Lambda	parameters: 43 body: 25
24	Literal
25	Conditional	value: 26 condition: 27
26	Operation	operator: 28 operands: 29
27	Operation	operator: 56 operands: 30
28	Literal
29	ExprTuple	31, 32
30	ExprTuple	33
31	Operation	operator: 34 operand: 39
32	Operation	operator: 36 operand: 40
33	ExprRange	lambda_map: 38 start_index: 62 end_index: 63
34	Literal
35	ExprTuple	39
36	Literal
37	ExprTuple	40
38	Lambda	parameter: 76 body: 41
39	Operation	operator: 42 operands: 43
40	Lambda	parameters: 44 body: 45
41	Operation	operator: 68 operands: 46
42	Literal
43	ExprTuple	47
44	ExprTuple	48
45	Conditional	value: 49 condition: 50
46	ExprTuple	70, 51
47	ExprRange	lambda_map: 52 start_index: 62 end_index: 63
48	ExprRange	lambda_map: 53 start_index: 62 end_index: 63
49	Operation	operator: 54 operands: 55
50	Operation	operator: 56 operands: 57
51	Variable
52	Lambda	parameter: 76 body: 70
53	Lambda	parameter: 76 body: 71
54	Literal
55	ExprTuple	58
56	Literal
57	ExprTuple	59
58	ExprRange	lambda_map: 60 start_index: 62 end_index: 63
59	ExprRange	lambda_map: 61 start_index: 62 end_index: 63
60	Lambda	parameter: 76 body: 64
61	Lambda	parameter: 76 body: 65
62	Literal
63	Variable
64	Operation	operator: 66 operands: 67
65	Operation	operator: 68 operands: 69
66	Literal
67	ExprTuple	71, 70
68	Literal
69	ExprTuple	71, 72
70	IndexedVar	variable: 73 index: 76
71	IndexedVar	variable: 74 index: 76
72	Variable
73	Variable
74	Variable
75	ExprTuple	76
76	Variable