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, lin_comb_axn
from proveit.logic import Equals, Forall, InSet, Set, SetOfAll
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(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(), 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} \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} \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: 49 body: 3
2	ExprTuple	49
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 54 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	49, 10
9	Lambda	parameters: 29 body: 11
10	Literal
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operands: 15
13	Operation	operator: 42 operands: 16
14	Literal
15	ExprTuple	17, 18
16	ExprTuple	19
17	Operation	operator: 20 operand: 25
18	Operation	operator: 22 operand: 26
19	ExprRange	lambda_map: 24 start_index: 48 end_index: 49
20	Literal
21	ExprTuple	25
22	Literal
23	ExprTuple	26
24	Lambda	parameter: 62 body: 27
25	Operation	operator: 28 operands: 29
26	Lambda	parameters: 30 body: 31
27	Operation	operator: 54 operands: 32
28	Literal
29	ExprTuple	33
30	ExprTuple	34
31	Conditional	value: 35 condition: 36
32	ExprTuple	56, 37
33	ExprRange	lambda_map: 38 start_index: 48 end_index: 49
34	ExprRange	lambda_map: 39 start_index: 48 end_index: 49
35	Operation	operator: 40 operands: 41
36	Operation	operator: 42 operands: 43
37	Variable
38	Lambda	parameter: 62 body: 56
39	Lambda	parameter: 62 body: 57
40	Literal
41	ExprTuple	44
42	Literal
43	ExprTuple	45
44	ExprRange	lambda_map: 46 start_index: 48 end_index: 49
45	ExprRange	lambda_map: 47 start_index: 48 end_index: 49
46	Lambda	parameter: 62 body: 50
47	Lambda	parameter: 62 body: 51
48	Literal
49	Variable
50	Operation	operator: 52 operands: 53
51	Operation	operator: 54 operands: 55
52	Literal
53	ExprTuple	57, 56
54	Literal
55	ExprTuple	57, 58
56	IndexedVar	variable: 59 index: 62
57	IndexedVar	variable: 60 index: 62
58	Variable
59	Variable
60	Variable
61	ExprTuple	62
62	Variable