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 Span, SpanningSets
from proveit.logic import And, Equals, InSet, 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, SpanningSets(V)), Equals(V, Span(sub_expr2))), 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\{\left(\left\{x_{1}, x_{2}, \ldots, x_{n}\right\} \in \textrm{SpanningSets}\left(V\right)\right) = \left(V = \textrm{Span}\left(\left\{x_{1}, x_{2}, \ldots, x_{n}\right\}\right)\right) \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: 27 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 12 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10
8	Operation	operator: 22 operands: 11
9	Operation	operator: 12 operands: 13
10	ExprRange	lambda_map: 14 start_index: 30 end_index: 31
11	ExprTuple	24, 15
12	Literal
13	ExprTuple	25, 16
14	Lambda	parameter: 35 body: 17
15	Operation	operator: 18 operand: 25
16	Operation	operator: 20 operand: 24
17	Operation	operator: 22 operands: 23
18	Literal
19	ExprTuple	25
20	Literal
21	ExprTuple	24
22	Literal
23	ExprTuple	32, 25
24	Operation	operator: 26 operands: 27
25	Variable
26	Literal
27	ExprTuple	28
28	ExprRange	lambda_map: 29 start_index: 30 end_index: 31
29	Lambda	parameter: 35 body: 32
30	Literal
31	Variable
32	IndexedVar	variable: 33 index: 35
33	Variable
34	ExprTuple	35
35	Variable