Expression of type Lambda

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, 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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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