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, H, Lambda, n, v, w
from proveit.core_expr_types import x_1_to_n
from proveit.linear_algebra import Bases, InnerProd, OrthoNormBases
from proveit.logic import And, Equals, Forall, InSet, Set
from proveit.numbers import KroneckerDelta, NaturalPos

# build up the expression from sub-expressions
sub_expr1 = Set(x_1_to_n)
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [x_1_to_n], instance_expr = Equals(InSet(sub_expr1, OrthoNormBases(H)), And(InSet(sub_expr1, Bases(H)), Forall(instance_param_or_params = [v, w], instance_expr = Equals(InnerProd(v, w), KroneckerDelta(v, w)), domain = sub_expr1))).with_wrapping_at(2), domain = H), InSet(n, NaturalPos)))

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())

n \mapsto \left\{\forall_{x_{1}, x_{2}, \ldots, x_{n} \in H}~\left(\begin{array}{c} \begin{array}{l} \left(\left\{x_{1}, x_{2}, \ldots, x_{n}\right\} \in \textrm{O.N.Bases}\left(H\right)\right) =  \\ \left(\left(\left\{x_{1}, x_{2}, \ldots, x_{n}\right\} \in \textrm{Bases}\left(H\right)\right) \land \left[\forall_{v, w \in \left\{x_{1}, x_{2}, \ldots, x_{n}\right\}}~\left(\left \langle v, w\right \rangle = \delta_{v, w}\right)\right]\right) \end{array} \end{array}\right) \textrm{ if } n \in \mathbb{N}^+\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 59 body: 2
1	ExprTuple	59
2	Conditional	value: 3 condition: 4
3	Operation	operator: 26 operand: 7
4	Operation	operator: 49 operands: 6
5	ExprTuple	7
6	ExprTuple	59, 8
7	Lambda	parameters: 55 body: 9
8	Literal
9	Conditional	value: 10 condition: 11
10	Operation	operator: 37 operands: 12
11	Operation	operator: 39 operands: 13
12	ExprTuple	14, 15
13	ExprTuple	16
14	Operation	operator: 49 operands: 17
15	Operation	operator: 39 operands: 18
16	ExprRange	lambda_map: 19 start_index: 58 end_index: 59
17	ExprTuple	53, 20
18	ExprTuple	21, 22
19	Lambda	parameter: 63 body: 23
20	Operation	operator: 24 operand: 34
21	Operation	operator: 49 operands: 25
22	Operation	operator: 26 operand: 30
23	Operation	operator: 49 operands: 28
24	Literal
25	ExprTuple	53, 29
26	Literal
27	ExprTuple	30
28	ExprTuple	60, 34
29	Operation	operator: 31 operand: 34
30	Lambda	parameters: 47 body: 33
31	Literal
32	ExprTuple	34
33	Conditional	value: 35 condition: 36
34	Variable
35	Operation	operator: 37 operands: 38
36	Operation	operator: 39 operands: 40
37	Literal
38	ExprTuple	41, 42
39	Literal
40	ExprTuple	43, 44
41	Operation	operator: 45 operands: 47
42	Operation	operator: 46 operands: 47
43	Operation	operator: 49 operands: 48
44	Operation	operator: 49 operands: 50
45	Literal
46	Literal
47	ExprTuple	51, 52
48	ExprTuple	51, 53
49	Literal
50	ExprTuple	52, 53
51	Variable
52	Variable
53	Operation	operator: 54 operands: 55
54	Literal
55	ExprTuple	56
56	ExprRange	lambda_map: 57 start_index: 58 end_index: 59
57	Lambda	parameter: 63 body: 60
58	Literal
59	Variable
60	IndexedVar	variable: 61 index: 63
61	Variable
62	ExprTuple	63
63	Variable