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