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
from proveit.core_expr_types import x_1_to_n
from proveit.linear_algebra import Dim, InnerProdSpaces, OrthoNormBases
from proveit.logic import And, Equals, Exists, InClass, InSet, Set

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(H, Conditional(Exists(instance_param_or_params = [x_1_to_n], instance_expr = InSet(Set(x_1_to_n), OrthoNormBases(H))), And(InClass(H, InnerProdSpaces(K)), Equals(Dim(H), n)))))

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\{\exists_{x_{1}, x_{2}, \ldots, x_{n}}~\left(\left\{x_{1}, x_{2}, \ldots, x_{n}\right\} \in \textrm{O.N.Bases}\left(H\right)\right) \textrm{ if } H \underset{{\scriptscriptstyle c}}{\in} \textrm{InnerProdSpaces}\left(K\right) ,  \textrm{Dim}\left(H\right) = 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: 32 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	10, 11
9	Lambda	parameters: 27 body: 12
10	Operation	operator: 13 operands: 14
11	Operation	operator: 15 operands: 16
12	Operation	operator: 17 operands: 18
13	Literal
14	ExprTuple	32, 19
15	Literal
16	ExprTuple	20, 35
17	Literal
18	ExprTuple	21, 22
19	Operation	operator: 23 operand: 30
20	Operation	operator: 25 operand: 32
21	Operation	operator: 26 operands: 27
22	Operation	operator: 28 operand: 32
23	Literal
24	ExprTuple	30
25	Literal
26	Literal
27	ExprTuple	31
28	Literal
29	ExprTuple	32
30	Variable
31	ExprRange	lambda_map: 33 start_index: 34 end_index: 35
32	Variable
33	Lambda	parameter: 39 body: 36
34	Literal
35	Variable
36	IndexedVar	variable: 37 index: 39
37	Variable
38	ExprTuple	39
39	Variable