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, Lambda, V, n
from proveit.core_expr_types import x_1_to_n
from proveit.linear_algebra import Bases, LinDepSets, SpanningSets
from proveit.logic import And, Equals, Forall, 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(n, Conditional(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(), 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} \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} \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: 46 body: 3
2	ExprTuple	46
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 32 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	46, 10
9	Lambda	parameters: 39 body: 11
10	Literal
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operands: 15
13	Operation	operator: 21 operands: 16
14	Literal
15	ExprTuple	17, 18
16	ExprTuple	19
17	Operation	operator: 32 operands: 20
18	Operation	operator: 21 operands: 22
19	ExprRange	lambda_map: 23 start_index: 45 end_index: 46
20	ExprTuple	35, 24
21	Literal
22	ExprTuple	25, 26
23	Lambda	parameter: 50 body: 27
24	Operation	operator: 28 operand: 43
25	Operation	operator: 32 operands: 29
26	Operation	operator: 30 operands: 31
27	Operation	operator: 32 operands: 33
28	Literal
29	ExprTuple	35, 34
30	Literal
31	ExprTuple	35, 36
32	Literal
33	ExprTuple	47, 43
34	Operation	operator: 37 operand: 43
35	Operation	operator: 38 operands: 39
36	Operation	operator: 40 operand: 43
37	Literal
38	Literal
39	ExprTuple	42
40	Literal
41	ExprTuple	43
42	ExprRange	lambda_map: 44 start_index: 45 end_index: 46
43	Variable
44	Lambda	parameter: 50 body: 47
45	Literal
46	Variable
47	IndexedVar	variable: 48 index: 50
48	Variable
49	ExprTuple	50
50	Variable