Expression of type Lambda

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, 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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	3
2	Conditional	value: 4 condition: 5
3	ExprRange	lambda_map: 6 start_index: 18 end_index: 19
4	Operation	operator: 20 operands: 7
5	Operation	operator: 8 operands: 9
6	Lambda	parameter: 31 body: 27
7	ExprTuple	10, 23
8	Literal
9	ExprTuple	11
10	Operation	operator: 12 operands: 13
11	ExprRange	lambda_map: 14 start_index: 18 end_index: 19
12	Literal
13	ExprTuple	15
14	Lambda	parameter: 31 body: 16
15	ExprRange	lambda_map: 17 start_index: 18 end_index: 19
16	Operation	operator: 20 operands: 21
17	Lambda	parameter: 31 body: 22
18	Literal
19	Variable
20	Literal
21	ExprTuple	27, 23
22	Operation	operator: 24 operands: 25
23	Variable
24	Literal
25	ExprTuple	26, 27
26	IndexedVar	variable: 28 index: 31
27	IndexedVar	variable: 29 index: 31
28	Variable
29	Variable
30	ExprTuple	31
31	Variable