Expression of type ExprTuple

from the theory of proveit.physics.quantum.QPE

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
from proveit.logic import Equals, InSet
from proveit.physics.quantum.QPE import _alpha_m_sqrd, _m_domain, _phase_est_circuit
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(m, Conditional(Equals(Prob(_phase_est_circuit), _alpha_m_sqrd), InSet(m, _m_domain))))

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\{\textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}\left(U, t\right)} & \meter & \multiqout{3}{\lvert m \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}\left(U, t\right)} & \measure{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array}\right) = \left|\alpha_{m}\right|^{2} \textrm{ if } m \in \{0~\ldotp \ldotp~2^{t} - 1\}\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: 108 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	108, 11
9	Operation	operator: 12 operand: 16
10	Operation	operator: 42 operands: 14
11	Operation	operator: 91 operands: 15
12	Literal
13	ExprTuple	16
14	ExprTuple	17, 53
15	ExprTuple	18, 19
16	Operation	operator: 20 operands: 21
17	Operation	operator: 22 operand: 29
18	Literal
19	Operation	operator: 105 operands: 24
20	Literal
21	ExprTuple	25, 26, 27, 28
22	Literal
23	ExprTuple	29
24	ExprTuple	30, 31
25	ExprTuple	32, 33
26	ExprTuple	34, 35
27	ExprTuple	36, 37
28	ExprTuple	38, 39
29	Operation	operator: 40 operand: 108
30	Operation	operator: 42 operands: 43
31	Operation	operator: 44 operand: 109
32	ExprRange	lambda_map: 46 start_index: 109 end_index: 110
33	ExprRange	lambda_map: 47 start_index: 109 end_index: 111
34	ExprRange	lambda_map: 48 start_index: 109 end_index: 110
35	ExprRange	lambda_map: 48 start_index: 98 end_index: 99
36	ExprRange	lambda_map: 49 start_index: 109 end_index: 110
37	ExprRange	lambda_map: 50 start_index: 109 end_index: 111
38	ExprRange	lambda_map: 51 start_index: 109 end_index: 110
39	ExprRange	lambda_map: 52 start_index: 109 end_index: 111
40	Literal
41	ExprTuple	108
42	Literal
43	ExprTuple	53, 110
44	Literal
45	ExprTuple	109
46	Lambda	parameter: 97 body: 54
47	Lambda	parameter: 97 body: 55
48	Lambda	parameter: 97 body: 56
49	Lambda	parameter: 97 body: 57
50	Lambda	parameter: 97 body: 58
51	Lambda	parameter: 97 body: 59
52	Lambda	parameter: 97 body: 61
53	Literal
54	Operation	operator: 83 operands: 62
55	Operation	operator: 69 operands: 63
56	Operation	operator: 69 operands: 64
57	Operation	operator: 65 operands: 66
58	Operation	operator: 84 operands: 67
59	Operation	operator: 69 operands: 68
60	ExprTuple	97
61	Operation	operator: 69 operands: 70
62	NamedExprs	state: 71
63	NamedExprs	element: 72 targets: 80
64	NamedExprs	element: 73 targets: 74
65	Literal
66	NamedExprs	basis: 75
67	NamedExprs	operation: 76
68	NamedExprs	element: 77 targets: 78
69	Literal
70	NamedExprs	element: 79 targets: 80
71	Operation	operator: 81 operand: 93
72	Operation	operator: 83 operands: 90
73	Operation	operator: 84 operands: 85
74	Operation	operator: 91 operands: 86
75	Literal
76	Literal
77	Operation	operator: 89 operands: 87
78	Operation	operator: 91 operands: 88
79	Operation	operator: 89 operands: 90
80	Operation	operator: 91 operands: 92
81	Literal
82	ExprTuple	93
83	Literal
84	Literal
85	NamedExprs	operation: 94 part: 97
86	ExprTuple	109, 99
87	NamedExprs	state: 95 part: 97
88	ExprTuple	109, 110
89	Literal
90	NamedExprs	state: 96 part: 97
91	Literal
92	ExprTuple	98, 99
93	Literal
94	Operation	operator: 100 operands: 101
95	Operation	operator: 102 operands: 103
96	Literal
97	Variable
98	Operation	operator: 105 operands: 104
99	Operation	operator: 105 operands: 106
100	Literal
101	ExprTuple	107, 110
102	Literal
103	ExprTuple	108, 110
104	ExprTuple	110, 109
105	Literal
106	ExprTuple	110, 111
107	Literal
108	Variable
109	Literal
110	Literal
111	Literal