Expression of type ExprTuple

from the theory of proveit.physics.quantum.circuits

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, m, n
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Abs, Exp, NaturalPos, two
from proveit.physics.quantum import NumBra, Qmult, m_bit_interval, m_ket_domain, normalized_var_ket_psi, var_ket_psi
from proveit.physics.quantum.circuits import register_meas
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(m, Conditional(Forall(instance_param_or_params = [n], instance_expr = Forall(instance_param_or_params = [var_ket_psi], instance_expr = Equals(Prob(register_meas), Exp(Abs(Qmult(NumBra(n, m), var_ket_psi)), two)), domain = m_ket_domain, condition = normalized_var_ket_psi), domain = m_bit_interval), InSet(m, NaturalPos))))

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(m \mapsto \left\{\forall_{n \in \{0~\ldotp \ldotp~2^{m} - 1\}}~\left[\forall_{\lvert \psi \rangle \in \mathbb{C}^{2^{m}}~|~\left \|\lvert \psi \rangle\right \| = 1}~\left(\textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\multiqin{3}{\lvert \psi \rangle} & \meter & \multiqout{3}{\lvert n \rangle_{m}} \\
\ghostqin{\lvert \psi \rangle} & \meter & \ghostqout{\lvert n \rangle_{m}} \\
\ghostqin{\lvert \psi \rangle} & \measure{\begin{array}{c}:\\ \left(m - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert n \rangle_{m}} \\
\ghostqin{\lvert \psi \rangle} & \meter & \ghostqout{\lvert n \rangle_{m}}
} \end{array}\right) = \left|{_{m}}\langle n \rvert \thinspace \lvert \psi \rangle\right|^{2}\right)\right] \textrm{ if } m \in \mathbb{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: 101 body: 3
2	ExprTuple	101
3	Conditional	value: 4 condition: 5
4	Operation	operator: 14 operand: 8
5	Operation	operator: 38 operands: 7
6	ExprTuple	8
7	ExprTuple	101, 9
8	Lambda	parameter: 100 body: 11
9	Literal
10	ExprTuple	100
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operand: 17
13	Operation	operator: 38 operands: 16
14	Literal
15	ExprTuple	17
16	ExprTuple	100, 18
17	Lambda	parameter: 94 body: 19
18	Operation	operator: 92 operands: 20
19	Conditional	value: 21 condition: 22
20	ExprTuple	23, 24
21	Operation	operator: 40 operands: 25
22	Operation	operator: 26 operands: 27
23	Literal
24	Operation	operator: 28 operands: 29
25	ExprTuple	30, 31
26	Literal
27	ExprTuple	32, 33
28	Literal
29	ExprTuple	61, 34
30	Operation	operator: 35 operand: 44
31	Operation	operator: 67 operands: 37
32	Operation	operator: 38 operands: 39
33	Operation	operator: 40 operands: 41
34	Operation	operator: 42 operand: 97
35	Literal
36	ExprTuple	44
37	ExprTuple	45, 73
38	Literal
39	ExprTuple	94, 46
40	Literal
41	ExprTuple	47, 97
42	Literal
43	ExprTuple	97
44	Operation	operator: 48 operands: 49
45	Operation	operator: 50 operand: 59
46	Operation	operator: 52 operands: 53
47	Operation	operator: 54 operand: 94
48	Literal
49	ExprTuple	56, 57, 58
50	Literal
51	ExprTuple	59
52	Literal
53	ExprTuple	60, 61
54	Literal
55	ExprTuple	94
56	ExprTuple	62
57	ExprTuple	63
58	ExprTuple	64
59	Operation	operator: 65 operands: 66
60	Literal
61	Operation	operator: 67 operands: 68
62	ExprRange	lambda_map: 69 start_index: 97 end_index: 101
63	ExprRange	lambda_map: 70 start_index: 97 end_index: 101
64	ExprRange	lambda_map: 71 start_index: 97 end_index: 101
65	Literal
66	ExprTuple	72, 94
67	Literal
68	ExprTuple	73, 101
69	Lambda	parameter: 96 body: 74
70	Lambda	parameter: 96 body: 75
71	Lambda	parameter: 96 body: 77
72	Operation	operator: 78 operands: 99
73	Literal
74	Operation	operator: 82 operands: 79
75	Operation	operator: 80 operands: 81
76	ExprTuple	96
77	Operation	operator: 82 operands: 83
78	Literal
79	NamedExprs	element: 84 targets: 87
80	Literal
81	NamedExprs	basis: 85
82	Literal
83	NamedExprs	element: 86 targets: 87
84	Operation	operator: 88 operands: 89
85	Literal
86	Operation	operator: 90 operands: 91
87	Operation	operator: 92 operands: 93
88	Literal
89	NamedExprs	state: 94 part: 96
90	Literal
91	NamedExprs	state: 95 part: 96
92	Literal
93	ExprTuple	97, 101
94	Variable
95	Operation	operator: 98 operands: 99
96	Variable
97	Literal
98	Literal
99	ExprTuple	100, 101
100	Variable
101	Variable