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, v
from proveit.core_expr_types import x_1_to_n
from proveit.linear_algebra import OrthoNormBases
from proveit.logic import And, Exists, InSet, Set

# build up the expression from sub-expressions
sub_expr1 = Set(x_1_to_n)
expr = Lambda(v, Conditional(Exists(instance_param_or_params = [x_1_to_n], instance_expr = And(InSet(v, sub_expr1), InSet(sub_expr1, OrthoNormBases(H))).with_wrapping_at(2)), InSet(v, H)))

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())

v \mapsto \left\{\exists_{x_{1}, x_{2}, \ldots, x_{n}}~\left(\begin{array}{c} \left(v \in \left\{x_{1}, x_{2}, \ldots, x_{n}\right\}\right) \land  \\ \left(\left\{x_{1}, x_{2}, \ldots, x_{n}\right\} \in \textrm{O.N.Bases}\left(H\right)\right) \end{array}\right) \textrm{ if } v \in H\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 17 body: 2
1	ExprTuple	17
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 15 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	17, 25
8	Lambda	parameters: 21 body: 9
9	Operation	operator: 10 operands: 11
10	Literal
11	ExprTuple	12, 13
12	Operation	operator: 15 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	18, 19
17	Variable
18	Operation	operator: 20 operands: 21
19	Operation	operator: 22 operand: 25
20	Literal
21	ExprTuple	24
22	Literal
23	ExprTuple	25
24	ExprRange	lambda_map: 26 start_index: 27 end_index: 28
25	Variable
26	Lambda	parameter: 32 body: 29
27	Literal
28	Variable
29	IndexedVar	variable: 30 index: 32
30	Variable
31	ExprTuple	32
32	Variable