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, Variable, a, 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 = 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} \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..

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