Expression of type Conditional

from the theory of proveit.linear_algebra.inner_products

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, v, w
from proveit.core_expr_types import x_1_to_n
from proveit.linear_algebra import InnerProd
from proveit.logic import And, Equals, InSet, Set
from proveit.numbers import KroneckerDelta

# build up the expression from sub-expressions
sub_expr1 = Set(x_1_to_n)
expr = Conditional(Equals(InnerProd(v, w), KroneckerDelta(v, w)), And(InSet(v, sub_expr1), InSet(w, sub_expr1)))

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 \langle v, w\right \rangle = \delta_{v, w} \textrm{ if } v \in \left\{x_{1}, x_{2}, \ldots, x_{n}\right\} ,  w \in \left\{x_{1}, x_{2}, \ldots, x_{n}\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: 13
8	Operation	operator: 12 operands: 13
9	Operation	operator: 15 operands: 14
10	Operation	operator: 15 operands: 16
11	Literal
12	Literal
13	ExprTuple	17, 18
14	ExprTuple	17, 19
15	Literal
16	ExprTuple	18, 19
17	Variable
18	Variable
19	Operation	operator: 20 operands: 21
20	Literal
21	ExprTuple	22
22	ExprRange	lambda_map: 23 start_index: 24 end_index: 25
23	Lambda	parameter: 29 body: 26
24	Literal
25	Variable
26	IndexedVar	variable: 27 index: 29
27	Variable
28	ExprTuple	29
29	Variable