Expression of type Exists

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 K, V
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 Equals, Exists

# build up the expression from sub-expressions
expr = 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()

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())

\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}

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	True	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 4 body: 5
4	ExprTuple	6
5	Conditional	value: 7 condition: 8
6	ExprRange	lambda_map: 9 start_index: 33 end_index: 34
7	Operation	operator: 10 operands: 11
8	Operation	operator: 12 operands: 13
9	Lambda	parameter: 48 body: 43
10	Literal
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	16, 17
14	Operation	operator: 18 operands: 19
15	Operation	operator: 20 operand: 26
16	ExprRange	lambda_map: 22 start_index: 33 end_index: 34
17	Operation	operator: 23 operands: 24
18	Literal
19	ExprTuple	25
20	Literal
21	ExprTuple	26
22	Lambda	parameter: 48 body: 27
23	Literal
24	ExprTuple	28
25	ExprRange	lambda_map: 29 start_index: 33 end_index: 34
26	Variable
27	Operation	operator: 30 operands: 31
28	ExprRange	lambda_map: 32 start_index: 33 end_index: 34
29	Lambda	parameter: 48 body: 35
30	Literal
31	ExprTuple	43, 36
32	Lambda	parameter: 48 body: 37
33	Literal
34	Variable
35	Operation	operator: 38 operands: 39
36	Variable
37	Operation	operator: 40 operands: 41
38	Literal
39	ExprTuple	43, 42
40	Literal
41	ExprTuple	43, 44
42	IndexedVar	variable: 45 index: 48
43	IndexedVar	variable: 46 index: 48
44	Literal
45	Variable
46	Variable
47	ExprTuple	48
48	Variable