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, 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 = ExprTuple(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())

\left(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..\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: 60 body: 3
2	ExprTuple	60
3	Conditional	value: 4 condition: 5
4	Operation	operator: 27 operand: 8
5	Operation	operator: 50 operands: 7
6	ExprTuple	8
7	ExprTuple	60, 9
8	Lambda	parameters: 56 body: 10
9	Literal
10	Conditional	value: 11 condition: 12
11	Operation	operator: 38 operands: 13
12	Operation	operator: 40 operands: 14
13	ExprTuple	15, 16
14	ExprTuple	17
15	Operation	operator: 50 operands: 18
16	Operation	operator: 40 operands: 19
17	ExprRange	lambda_map: 20 start_index: 59 end_index: 60
18	ExprTuple	54, 21
19	ExprTuple	22, 23
20	Lambda	parameter: 64 body: 24
21	Operation	operator: 25 operand: 35
22	Operation	operator: 50 operands: 26
23	Operation	operator: 27 operand: 31
24	Operation	operator: 50 operands: 29
25	Literal
26	ExprTuple	54, 30
27	Literal
28	ExprTuple	31
29	ExprTuple	61, 35
30	Operation	operator: 32 operand: 35
31	Lambda	parameters: 48 body: 34
32	Literal
33	ExprTuple	35
34	Conditional	value: 36 condition: 37
35	Variable
36	Operation	operator: 38 operands: 39
37	Operation	operator: 40 operands: 41
38	Literal
39	ExprTuple	42, 43
40	Literal
41	ExprTuple	44, 45
42	Operation	operator: 46 operands: 48
43	Operation	operator: 47 operands: 48
44	Operation	operator: 50 operands: 49
45	Operation	operator: 50 operands: 51
46	Literal
47	Literal
48	ExprTuple	52, 53
49	ExprTuple	52, 54
50	Literal
51	ExprTuple	53, 54
52	Variable
53	Variable
54	Operation	operator: 55 operands: 56
55	Literal
56	ExprTuple	57
57	ExprRange	lambda_map: 58 start_index: 59 end_index: 60
58	Lambda	parameter: 64 body: 61
59	Literal
60	Variable
61	IndexedVar	variable: 62 index: 64
62	Variable
63	ExprTuple	64
64	Variable