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

# build up the expression from sub-expressions
sub_expr1 = Set(x_1_to_n)
expr = ExprTuple(Lambda(H, Conditional(Forall(instance_param_or_params = [n], instance_expr = 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), domain = NaturalPos), InClass(H, InnerProdSpaces(K)))))

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(H \mapsto \left\{\forall_{n \in \mathbb{N}^+}~\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)\right] \textrm{ if } H \underset{{\scriptscriptstyle c}}{\in} \textrm{InnerProdSpaces}\left(K\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	parameter: 46 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 38 operand: 8
4	Operation	operator: 6 operands: 7
5	ExprTuple	8
6	Literal
7	ExprTuple	46, 9
8	Lambda	parameter: 71 body: 11
9	Operation	operator: 12 operand: 16
10	ExprTuple	71
11	Conditional	value: 14 condition: 15
12	Literal
13	ExprTuple	16
14	Operation	operator: 38 operand: 19
15	Operation	operator: 61 operands: 18
16	Variable
17	ExprTuple	19
18	ExprTuple	71, 20
19	Lambda	parameters: 67 body: 21
20	Literal
21	Conditional	value: 22 condition: 23
22	Operation	operator: 49 operands: 24
23	Operation	operator: 51 operands: 25
24	ExprTuple	26, 27
25	ExprTuple	28
26	Operation	operator: 61 operands: 29
27	Operation	operator: 51 operands: 30
28	ExprRange	lambda_map: 31 start_index: 70 end_index: 71
29	ExprTuple	65, 32
30	ExprTuple	33, 34
31	Lambda	parameter: 75 body: 35
32	Operation	operator: 36 operand: 46
33	Operation	operator: 61 operands: 37
34	Operation	operator: 38 operand: 42
35	Operation	operator: 61 operands: 40
36	Literal
37	ExprTuple	65, 41
38	Literal
39	ExprTuple	42
40	ExprTuple	72, 46
41	Operation	operator: 43 operand: 46
42	Lambda	parameters: 59 body: 45
43	Literal
44	ExprTuple	46
45	Conditional	value: 47 condition: 48
46	Variable
47	Operation	operator: 49 operands: 50
48	Operation	operator: 51 operands: 52
49	Literal
50	ExprTuple	53, 54
51	Literal
52	ExprTuple	55, 56
53	Operation	operator: 57 operands: 59
54	Operation	operator: 58 operands: 59
55	Operation	operator: 61 operands: 60
56	Operation	operator: 61 operands: 62
57	Literal
58	Literal
59	ExprTuple	63, 64
60	ExprTuple	63, 65
61	Literal
62	ExprTuple	64, 65
63	Variable
64	Variable
65	Operation	operator: 66 operands: 67
66	Literal
67	ExprTuple	68
68	ExprRange	lambda_map: 69 start_index: 70 end_index: 71
69	Lambda	parameter: 75 body: 72
70	Literal
71	Variable
72	IndexedVar	variable: 73 index: 75
73	Variable
74	ExprTuple	75
75	Variable