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 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, 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(K, Forall(instance_param_or_params = [H], instance_expr = 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), domain = 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(K \mapsto \left[\forall_{H \underset{{\scriptscriptstyle c}}{\in} \textrm{InnerProdSpaces}\left(K\right)}~\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]\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: 19 body: 2
2	Operation	operator: 41 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 49 body: 5
5	Conditional	value: 6 condition: 7
6	Operation	operator: 41 operand: 11
7	Operation	operator: 9 operands: 10
8	ExprTuple	11
9	Literal
10	ExprTuple	49, 12
11	Lambda	parameter: 74 body: 14
12	Operation	operator: 15 operand: 19
13	ExprTuple	74
14	Conditional	value: 17 condition: 18
15	Literal
16	ExprTuple	19
17	Operation	operator: 41 operand: 22
18	Operation	operator: 64 operands: 21
19	Variable
20	ExprTuple	22
21	ExprTuple	74, 23
22	Lambda	parameters: 70 body: 24
23	Literal
24	Conditional	value: 25 condition: 26
25	Operation	operator: 52 operands: 27
26	Operation	operator: 54 operands: 28
27	ExprTuple	29, 30
28	ExprTuple	31
29	Operation	operator: 64 operands: 32
30	Operation	operator: 54 operands: 33
31	ExprRange	lambda_map: 34 start_index: 73 end_index: 74
32	ExprTuple	68, 35
33	ExprTuple	36, 37
34	Lambda	parameter: 78 body: 38
35	Operation	operator: 39 operand: 49
36	Operation	operator: 64 operands: 40
37	Operation	operator: 41 operand: 45
38	Operation	operator: 64 operands: 43
39	Literal
40	ExprTuple	68, 44
41	Literal
42	ExprTuple	45
43	ExprTuple	75, 49
44	Operation	operator: 46 operand: 49
45	Lambda	parameters: 62 body: 48
46	Literal
47	ExprTuple	49
48	Conditional	value: 50 condition: 51
49	Variable
50	Operation	operator: 52 operands: 53
51	Operation	operator: 54 operands: 55
52	Literal
53	ExprTuple	56, 57
54	Literal
55	ExprTuple	58, 59
56	Operation	operator: 60 operands: 62
57	Operation	operator: 61 operands: 62
58	Operation	operator: 64 operands: 63
59	Operation	operator: 64 operands: 65
60	Literal
61	Literal
62	ExprTuple	66, 67
63	ExprTuple	66, 68
64	Literal
65	ExprTuple	67, 68
66	Variable
67	Variable
68	Operation	operator: 69 operands: 70
69	Literal
70	ExprTuple	71
71	ExprRange	lambda_map: 72 start_index: 73 end_index: 74
72	Lambda	parameter: 78 body: 75
73	Literal
74	Variable
75	IndexedVar	variable: 76 index: 78
76	Variable
77	ExprTuple	78
78	Variable