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, V, Variable, n, x
from proveit.core_expr_types import a_1_to_n, x_1_to_n
from proveit.linear_algebra import LinDepSets, VecZero, lin_comb_axn, some_nonzero_a
from proveit.logic import And, Equals, Exists, InSet, Set
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(Equals(InSet(Set(x_1_to_n), LinDepSets(V)), Exists(instance_param_or_params = [a_1_to_n], instance_expr = Equals(lin_comb_axn, VecZero(V)), domain = K, condition = some_nonzero_a).with_wrapping()).with_wrapping_at(2), 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\{\begin{array}{c} \begin{array}{l} \left(\left\{x_{1}, x_{2}, \ldots, x_{n}\right\} \in \textrm{LinDepSets}\left(V\right)\right) =  \\ \left[\begin{array}{l}\exists_{a_{1}, a_{2}, \ldots, a_{n} \in K~|~\left(a_{1} \neq 0\right) \lor  \left(a_{2} \neq 0\right) \lor  \ldots \lor  \left(a_{n} \neq 0\right)}~\\
\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)\right)\end{array}\right] \end{array} \end{array} \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: 18 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 29 operands: 4
3	Operation	operator: 31 operands: 5
4	ExprTuple	6, 7
5	ExprTuple	8
6	Operation	operator: 49 operands: 9
7	Operation	operator: 10 operand: 15
8	ExprRange	lambda_map: 12 start_index: 52 end_index: 53
9	ExprTuple	13, 14
10	Literal
11	ExprTuple	15
12	Lambda	parameter: 67 body: 16
13	Operation	operator: 17 operands: 18
14	Operation	operator: 19 operand: 45
15	Lambda	parameters: 20 body: 21
16	Operation	operator: 49 operands: 22
17	Literal
18	ExprTuple	23
19	Literal
20	ExprTuple	24
21	Conditional	value: 25 condition: 26
22	ExprTuple	61, 45
23	ExprRange	lambda_map: 27 start_index: 52 end_index: 53
24	ExprRange	lambda_map: 28 start_index: 52 end_index: 53
25	Operation	operator: 29 operands: 30
26	Operation	operator: 31 operands: 32
27	Lambda	parameter: 67 body: 61
28	Lambda	parameter: 67 body: 62
29	Literal
30	ExprTuple	33, 34
31	Literal
32	ExprTuple	35, 36
33	Operation	operator: 37 operands: 38
34	Operation	operator: 39 operand: 45
35	ExprRange	lambda_map: 41 start_index: 52 end_index: 53
36	Operation	operator: 42 operands: 43
37	Literal
38	ExprTuple	44
39	Literal
40	ExprTuple	45
41	Lambda	parameter: 67 body: 46
42	Literal
43	ExprTuple	47
44	ExprRange	lambda_map: 48 start_index: 52 end_index: 53
45	Variable
46	Operation	operator: 49 operands: 50
47	ExprRange	lambda_map: 51 start_index: 52 end_index: 53
48	Lambda	parameter: 67 body: 54
49	Literal
50	ExprTuple	62, 55
51	Lambda	parameter: 67 body: 56
52	Literal
53	Variable
54	Operation	operator: 57 operands: 58
55	Variable
56	Operation	operator: 59 operands: 60
57	Literal
58	ExprTuple	62, 61
59	Literal
60	ExprTuple	62, 63
61	IndexedVar	variable: 64 index: 67
62	IndexedVar	variable: 65 index: 67
63	Literal
64	Variable
65	Variable
66	ExprTuple	67
67	Variable