Expression of type ExprTuple

from the theory of proveit.linear_algebra.scalar_multiplication

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