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, V, Variable, a, n
from proveit.core_expr_types import a_1_to_n
from proveit.linear_algebra import VecZero, lin_comb_axn, some_nonzero_a
from proveit.logic import And, Equals, 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(Equals(lin_comb_axn, VecZero(V)), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), K), one, n), some_nonzero_a))))

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(\left(a_{1} \cdot x_{1}\right) +  \left(a_{2} \cdot x_{2}\right) +  \ldots +  \left(a_{n} \cdot x_{n}\right)\right) = \vec{0}\left(V\right) \textrm{ if } \left(a_{1} \in K\right) ,  \left(a_{2} \in K\right) ,  \ldots ,  \left(a_{n} \in K\right) ,  \left(a_{1} \neq 0\right) \lor  \left(a_{2} \neq 0\right) \lor  \ldots \lor  \left(a_{n} \neq 0\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: 31 end_index: 32
5	Operation	operator: 8 operands: 9
6	Operation	operator: 10 operands: 11
7	Lambda	parameter: 46 body: 41
8	Literal
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	14, 15
12	Operation	operator: 16 operands: 17
13	Operation	operator: 18 operand: 24
14	ExprRange	lambda_map: 20 start_index: 31 end_index: 32
15	Operation	operator: 21 operands: 22
16	Literal
17	ExprTuple	23
18	Literal
19	ExprTuple	24
20	Lambda	parameter: 46 body: 25
21	Literal
22	ExprTuple	26
23	ExprRange	lambda_map: 27 start_index: 31 end_index: 32
24	Variable
25	Operation	operator: 28 operands: 29
26	ExprRange	lambda_map: 30 start_index: 31 end_index: 32
27	Lambda	parameter: 46 body: 33
28	Literal
29	ExprTuple	41, 34
30	Lambda	parameter: 46 body: 35
31	Literal
32	Variable
33	Operation	operator: 36 operands: 37
34	Variable
35	Operation	operator: 38 operands: 39
36	Literal
37	ExprTuple	41, 40
38	Literal
39	ExprTuple	41, 42
40	IndexedVar	variable: 43 index: 46
41	IndexedVar	variable: 44 index: 46
42	Literal
43	Variable
44	Variable
45	ExprTuple	46
46	Variable