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 x_1_to_n
from proveit.linear_algebra import Bases, LinDepSets, SpanningSets, VecSpaces
from proveit.logic import And, Equals, Forall, InClass, InSet, NotInSet, Set
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
sub_expr1 = Set(x_1_to_n)
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(InSet(sub_expr1, Bases(V)), And(InSet(sub_expr1, SpanningSets(V)), NotInSet(sub_expr1, LinDepSets(V))).with_wrapping_at(2)).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} \left(\left\{x_{1}, x_{2}, \ldots, x_{n}\right\} \in \textrm{Bases}\left(V\right)\right) =  \\ \left(\begin{array}{c} \left(\left\{x_{1}, x_{2}, \ldots, x_{n}\right\} \in \textrm{SpanningSets}\left(V\right)\right) \land  \\ \left(\left\{x_{1}, x_{2}, \ldots, x_{n}\right\} \notin \textrm{LinDepSets}\left(V\right)\right) \end{array}\right) \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: 54 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 17 operand: 8
4	Operation	operator: 6 operands: 7
5	ExprTuple	8
6	Literal
7	ExprTuple	54, 9
8	Lambda	parameter: 57 body: 11
9	Operation	operator: 12 operand: 16
10	ExprTuple	57
11	Conditional	value: 14 condition: 15
12	Literal
13	ExprTuple	16
14	Operation	operator: 17 operand: 20
15	Operation	operator: 43 operands: 19
16	Variable
17	Literal
18	ExprTuple	20
19	ExprTuple	57, 21
20	Lambda	parameters: 50 body: 22
21	Literal
22	Conditional	value: 23 condition: 24
23	Operation	operator: 25 operands: 26
24	Operation	operator: 32 operands: 27
25	Literal
26	ExprTuple	28, 29
27	ExprTuple	30
28	Operation	operator: 43 operands: 31
29	Operation	operator: 32 operands: 33
30	ExprRange	lambda_map: 34 start_index: 56 end_index: 57
31	ExprTuple	46, 35
32	Literal
33	ExprTuple	36, 37
34	Lambda	parameter: 61 body: 38
35	Operation	operator: 39 operand: 54
36	Operation	operator: 43 operands: 40
37	Operation	operator: 41 operands: 42
38	Operation	operator: 43 operands: 44
39	Literal
40	ExprTuple	46, 45
41	Literal
42	ExprTuple	46, 47
43	Literal
44	ExprTuple	58, 54
45	Operation	operator: 48 operand: 54
46	Operation	operator: 49 operands: 50
47	Operation	operator: 51 operand: 54
48	Literal
49	Literal
50	ExprTuple	53
51	Literal
52	ExprTuple	54
53	ExprRange	lambda_map: 55 start_index: 56 end_index: 57
54	Variable
55	Lambda	parameter: 61 body: 58
56	Literal
57	Variable
58	IndexedVar	variable: 59 index: 61
59	Variable
60	ExprTuple	61
61	Variable