Expression of type ExprTuple

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, ExprTuple, Lambda, 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 = ExprTuple(Lambda([v, w], 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(v, w\right) \mapsto \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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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