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, X, i, n
from proveit.core_expr_types import x_1_to_n, x_i
from proveit.linear_algebra import HilbertSpaces, Hspace, OrthoNormBases, OrthoProj, VecSum
from proveit.logic import Equals, Forall, InClass, InSet, SubsetEq
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 = [X], instance_expr = Forall(instance_param_or_params = [n], instance_expr = Forall(instance_param_or_params = [x_1_to_n], instance_expr = Equals(OrthoProj(Hspace, X), VecSum(index_or_indices = [i], summand = Qmult(Ket(x_i), Bra(x_i)), domain = Interval(one, n))), condition = InSet(x_1_to_n_kets, OrthoNormBases(Hspace))).with_wrapping(), domain = NaturalPos), condition = SubsetEq(X, Hspace)), 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_{X~|~X \subseteq \mathcal{H}}~\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(\textrm{OrthoProj}\left(\mathcal{H}, X\right) = \left(\sum_{i=1}^{n} \left(\lvert x_{i} \rangle \thinspace \langle x_{i} \rvert\right)\right)\right)\end{array}\right]\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: 51 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 22 operand: 8
4	Operation	operator: 6 operands: 7
5	ExprTuple	8
6	Literal
7	ExprTuple	51, 9
8	Lambda	parameter: 48 body: 11
9	Literal
10	ExprTuple	48
11	Conditional	value: 12 condition: 13
12	Operation	operator: 22 operand: 17
13	Operation	operator: 15 operands: 16
14	ExprTuple	17
15	Literal
16	ExprTuple	48, 51
17	Lambda	parameter: 74 body: 19
18	ExprTuple	74
19	Conditional	value: 20 condition: 21
20	Operation	operator: 22 operand: 25
21	Operation	operator: 59 operands: 24
22	Literal
23	ExprTuple	25
24	ExprTuple	74, 26
25	Lambda	parameters: 27 body: 28
26	Literal
27	ExprTuple	29
28	Conditional	value: 30 condition: 31
29	ExprRange	lambda_map: 32 start_index: 73 end_index: 74
30	Operation	operator: 33 operands: 34
31	Operation	operator: 59 operands: 35
32	Lambda	parameter: 75 body: 65
33	Literal
34	ExprTuple	36, 37
35	ExprTuple	38, 39
36	Operation	operator: 40 operands: 41
37	Operation	operator: 42 operand: 49
38	Operation	operator: 44 operands: 45
39	Operation	operator: 46 operand: 51
40	Literal
41	ExprTuple	51, 48
42	Literal
43	ExprTuple	49
44	Literal
45	ExprTuple	50
46	Literal
47	ExprTuple	51
48	Variable
49	Lambda	parameter: 78 body: 52
50	ExprRange	lambda_map: 53 start_index: 73 end_index: 74
51	Variable
52	Conditional	value: 54 condition: 55
53	Lambda	parameter: 75 body: 56
54	Operation	operator: 57 operands: 58
55	Operation	operator: 59 operands: 60
56	Operation	operator: 66 operand: 65
57	Literal
58	ExprTuple	62, 63
59	Literal
60	ExprTuple	78, 64
61	ExprTuple	65
62	Operation	operator: 66 operand: 72
63	Operation	operator: 67 operand: 72
64	Operation	operator: 69 operands: 70
65	IndexedVar	variable: 76 index: 75
66	Literal
67	Literal
68	ExprTuple	72
69	Literal
70	ExprTuple	73, 74
71	ExprTuple	75
72	IndexedVar	variable: 76 index: 78
73	Literal
74	Variable
75	Variable
76	Variable
77	ExprTuple	78
78	Variable