Expression of type ExprTuple

from the theory of proveit.physics.quantum.algebra

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, Lambda, i, n
from proveit.core_expr_types import x_1_to_n, x_i
from proveit.linear_algebra import HilbertSpaces, Hspace, Identity, OrthoNormBases, VecSum
from proveit.logic import Equals, Forall, InClass, InSet
from proveit.numbers import Interval, NaturalPos, one
from proveit.physics.quantum import Bra, Ket, Qmult
from proveit.physics.quantum.algebra import x_1_to_n_kets

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(Hspace, Conditional(Forall(instance_param_or_params = [n], instance_expr = Forall(instance_param_or_params = [x_1_to_n], instance_expr = Equals(VecSum(index_or_indices = [i], summand = Qmult(Ket(x_i), Bra(x_i)), domain = Interval(one, n)), Identity(Hspace)), condition = InSet(x_1_to_n_kets, OrthoNormBases(Hspace))).with_wrapping(), domain = NaturalPos), InClass(Hspace, HilbertSpaces))))

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(\mathcal{H} \mapsto \left\{\forall_{n \in \mathbb{N}^+}~\left[\begin{array}{l}\forall_{x_{1}, x_{2}, \ldots, x_{n}~|~\left\{\lvert x_{1} \rangle, \lvert x_{2} \rangle, \ldots, \lvert x_{n} \rangle\right\} \in \textrm{O.N.Bases}\left(\mathcal{H}\right)}~\\
\left(\left(\sum_{i=1}^{n} \left(\lvert x_{i} \rangle \thinspace \langle x_{i} \rvert\right)\right) = I_{\mathcal{H}}\right)\end{array}\right] \textrm{ if } \mathcal{H} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}\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: 41 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 14 operand: 8
4	Operation	operator: 6 operands: 7
5	ExprTuple	8
6	Literal
7	ExprTuple	41, 9
8	Lambda	parameter: 64 body: 11
9	Literal
10	ExprTuple	64
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operand: 17
13	Operation	operator: 49 operands: 16
14	Literal
15	ExprTuple	17
16	ExprTuple	64, 18
17	Lambda	parameters: 19 body: 20
18	Literal
19	ExprTuple	21
20	Conditional	value: 22 condition: 23
21	ExprRange	lambda_map: 24 start_index: 63 end_index: 64
22	Operation	operator: 25 operands: 26
23	Operation	operator: 49 operands: 27
24	Lambda	parameter: 65 body: 55
25	Literal
26	ExprTuple	28, 29
27	ExprTuple	30, 31
28	Operation	operator: 32 operand: 39
29	Operation	operator: 34 operand: 41
30	Operation	operator: 35 operands: 36
31	Operation	operator: 37 operand: 41
32	Literal
33	ExprTuple	39
34	Literal
35	Literal
36	ExprTuple	40
37	Literal
38	ExprTuple	41
39	Lambda	parameter: 68 body: 42
40	ExprRange	lambda_map: 43 start_index: 63 end_index: 64
41	Variable
42	Conditional	value: 44 condition: 45
43	Lambda	parameter: 65 body: 46
44	Operation	operator: 47 operands: 48
45	Operation	operator: 49 operands: 50
46	Operation	operator: 56 operand: 55
47	Literal
48	ExprTuple	52, 53
49	Literal
50	ExprTuple	68, 54
51	ExprTuple	55
52	Operation	operator: 56 operand: 62
53	Operation	operator: 57 operand: 62
54	Operation	operator: 59 operands: 60
55	IndexedVar	variable: 66 index: 65
56	Literal
57	Literal
58	ExprTuple	62
59	Literal
60	ExprTuple	63, 64
61	ExprTuple	65
62	IndexedVar	variable: 66 index: 68
63	Literal
64	Variable
65	Variable
66	Variable
67	ExprTuple	68
68	Variable