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, Lambda, V, Variable, n, x
from proveit.core_expr_types import x_1_to_n
from proveit.linear_algebra import Bases, LinDepSets, SpanningSets
from proveit.logic import And, Equals, InSet, NotInSet, Set
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Set(x_1_to_n)
expr = ExprTuple(Lambda([x_1_to_n], Conditional(Equals(InSet(sub_expr2, Bases(V)), And(InSet(sub_expr2, SpanningSets(V)), NotInSet(sub_expr2, LinDepSets(V))).with_wrapping_at(2)).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} \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} \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: 30 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 12 operands: 7
5	Literal
6	ExprTuple	8, 9
7	ExprTuple	10
8	Operation	operator: 23 operands: 11
9	Operation	operator: 12 operands: 13
10	ExprRange	lambda_map: 14 start_index: 36 end_index: 37
11	ExprTuple	26, 15
12	Literal
13	ExprTuple	16, 17
14	Lambda	parameter: 41 body: 18
15	Operation	operator: 19 operand: 34
16	Operation	operator: 23 operands: 20
17	Operation	operator: 21 operands: 22
18	Operation	operator: 23 operands: 24
19	Literal
20	ExprTuple	26, 25
21	Literal
22	ExprTuple	26, 27
23	Literal
24	ExprTuple	38, 34
25	Operation	operator: 28 operand: 34
26	Operation	operator: 29 operands: 30
27	Operation	operator: 31 operand: 34
28	Literal
29	Literal
30	ExprTuple	33
31	Literal
32	ExprTuple	34
33	ExprRange	lambda_map: 35 start_index: 36 end_index: 37
34	Variable
35	Lambda	parameter: 41 body: 38
36	Literal
37	Variable
38	IndexedVar	variable: 39 index: 41
39	Variable
40	ExprTuple	41
41	Variable