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, 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 = ExprTuple(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(\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..\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: 16 end_index: 17
5	Operation	operator: 8 operands: 9
6	Operation	operator: 10 operands: 11
7	Lambda	parameter: 30 body: 25
8	Literal
9	ExprTuple	12
10	Literal
11	ExprTuple	13
12	ExprRange	lambda_map: 14 start_index: 16 end_index: 17
13	ExprRange	lambda_map: 15 start_index: 16 end_index: 17
14	Lambda	parameter: 30 body: 18
15	Lambda	parameter: 30 body: 19
16	Literal
17	Variable
18	Operation	operator: 20 operands: 21
19	Operation	operator: 22 operands: 23
20	Literal
21	ExprTuple	25, 24
22	Literal
23	ExprTuple	25, 26
24	IndexedVar	variable: 27 index: 30
25	IndexedVar	variable: 28 index: 30
26	Variable
27	Variable
28	Variable
29	ExprTuple	30
30	Variable