Expression of type Conditional

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, V, Variable, a, 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 = 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(\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..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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