Expression of type Lambda

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, IndexedVar, K, Lambda, Variable, a, n
from proveit.core_expr_types import a_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([a_1_to_n], Conditional(lin_comb_axn, And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), K), 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(a_{1}, a_{2}, \ldots, a_{n}\right) \mapsto \left\{\left(a_{1} \cdot x_{1}\right) +  \left(a_{2} \cdot x_{2}\right) +  \ldots +  \left(a_{n} \cdot x_{n}\right) \textrm{ if } \left(a_{1} \in K\right) \land  \left(a_{2} \in K\right) \land  \ldots \land  \left(a_{n} \in K\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: 15 end_index: 16
4	Operation	operator: 7 operands: 8
5	Operation	operator: 9 operands: 10
6	Lambda	parameter: 29 body: 24
7	Literal
8	ExprTuple	11
9	Literal
10	ExprTuple	12
11	ExprRange	lambda_map: 13 start_index: 15 end_index: 16
12	ExprRange	lambda_map: 14 start_index: 15 end_index: 16
13	Lambda	parameter: 29 body: 17
14	Lambda	parameter: 29 body: 18
15	Literal
16	Variable
17	Operation	operator: 19 operands: 20
18	Operation	operator: 21 operands: 22
19	Literal
20	ExprTuple	24, 23
21	Literal
22	ExprTuple	24, 25
23	IndexedVar	variable: 26 index: 29
24	IndexedVar	variable: 27 index: 29
25	Variable
26	Variable
27	Variable
28	ExprTuple	29
29	Variable