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, ExprRange, ExprTuple, H, IndexedVar, Lambda, Variable, n, v, w, x
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, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Set(x_1_to_n)
expr = ExprTuple(Lambda([x_1_to_n], Conditional(Equals(InSet(sub_expr2, OrthoNormBases(H)), And(InSet(sub_expr2, Bases(H)), Forall(instance_param_or_params = [v, w], instance_expr = Equals(InnerProd(v, w), KroneckerDelta(v, w)), domain = sub_expr2))).with_wrapping_at(2), And(ExprRange(sub_expr1, InSet(IndexedVar(x, sub_expr1), H), one, 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(\left(x_{1}, x_{2}, \ldots, x_{n}\right) \mapsto \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} \textrm{ if } \left(x_{1} \in H\right) \land  \left(x_{2} \in H\right) \land  \ldots \land  \left(x_{n} \in H\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	parameters: 48 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 30 operands: 5
4	Operation	operator: 32 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	9
7	Operation	operator: 42 operands: 10
8	Operation	operator: 32 operands: 11
9	ExprRange	lambda_map: 12 start_index: 51 end_index: 52
10	ExprTuple	46, 13
11	ExprTuple	14, 15
12	Lambda	parameter: 56 body: 16
13	Operation	operator: 17 operand: 27
14	Operation	operator: 42 operands: 18
15	Operation	operator: 19 operand: 23
16	Operation	operator: 42 operands: 21
17	Literal
18	ExprTuple	46, 22
19	Literal
20	ExprTuple	23
21	ExprTuple	53, 27
22	Operation	operator: 24 operand: 27
23	Lambda	parameters: 40 body: 26
24	Literal
25	ExprTuple	27
26	Conditional	value: 28 condition: 29
27	Variable
28	Operation	operator: 30 operands: 31
29	Operation	operator: 32 operands: 33
30	Literal
31	ExprTuple	34, 35
32	Literal
33	ExprTuple	36, 37
34	Operation	operator: 38 operands: 40
35	Operation	operator: 39 operands: 40
36	Operation	operator: 42 operands: 41
37	Operation	operator: 42 operands: 43
38	Literal
39	Literal
40	ExprTuple	44, 45
41	ExprTuple	44, 46
42	Literal
43	ExprTuple	45, 46
44	Variable
45	Variable
46	Operation	operator: 47 operands: 48
47	Literal
48	ExprTuple	49
49	ExprRange	lambda_map: 50 start_index: 51 end_index: 52
50	Lambda	parameter: 56 body: 53
51	Literal
52	Variable
53	IndexedVar	variable: 54 index: 56
54	Variable
55	ExprTuple	56
56	Variable