Expression of type Equals

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 Lambda, m
from proveit.logic import Equals, Image
from proveit.physics.quantum.QPE import _Omega, _m_domain, _phase_est_circuit

# build up the expression from sub-expressions
expr = Equals(Image(Lambda(m, _phase_est_circuit), _m_domain), _Omega)

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(\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)\right]^{\rightarrow}(\{0~\ldotp \ldotp~2^{t} - 1\}) = \Omega

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 5 operands: 6
4	Literal
5	Literal
6	ExprTuple	7, 8
7	Lambda	parameter: 97 body: 10
8	Operation	operator: 80 operands: 11
9	ExprTuple	97
10	Operation	operator: 12 operands: 13
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	16, 17, 18, 19
14	Literal
15	Operation	operator: 94 operands: 20
16	ExprTuple	21, 22
17	ExprTuple	23, 24
18	ExprTuple	25, 26
19	ExprTuple	27, 28
20	ExprTuple	29, 30
21	ExprRange	lambda_map: 31 start_index: 98 end_index: 99
22	ExprRange	lambda_map: 32 start_index: 98 end_index: 100
23	ExprRange	lambda_map: 33 start_index: 98 end_index: 99
24	ExprRange	lambda_map: 33 start_index: 87 end_index: 88
25	ExprRange	lambda_map: 34 start_index: 98 end_index: 99
26	ExprRange	lambda_map: 35 start_index: 98 end_index: 100
27	ExprRange	lambda_map: 36 start_index: 98 end_index: 99
28	ExprRange	lambda_map: 37 start_index: 98 end_index: 100
29	Operation	operator: 38 operands: 39
30	Operation	operator: 40 operand: 98
31	Lambda	parameter: 86 body: 42
32	Lambda	parameter: 86 body: 43
33	Lambda	parameter: 86 body: 44
34	Lambda	parameter: 86 body: 45
35	Lambda	parameter: 86 body: 46
36	Lambda	parameter: 86 body: 47
37	Lambda	parameter: 86 body: 49
38	Literal
39	ExprTuple	50, 99
40	Literal
41	ExprTuple	98
42	Operation	operator: 72 operands: 51
43	Operation	operator: 58 operands: 52
44	Operation	operator: 58 operands: 53
45	Operation	operator: 54 operands: 55
46	Operation	operator: 73 operands: 56
47	Operation	operator: 58 operands: 57
48	ExprTuple	86
49	Operation	operator: 58 operands: 59
50	Literal
51	NamedExprs	state: 60
52	NamedExprs	element: 61 targets: 69
53	NamedExprs	element: 62 targets: 63
54	Literal
55	NamedExprs	basis: 64
56	NamedExprs	operation: 65
57	NamedExprs	element: 66 targets: 67
58	Literal
59	NamedExprs	element: 68 targets: 69
60	Operation	operator: 70 operand: 82
61	Operation	operator: 72 operands: 79
62	Operation	operator: 73 operands: 74
63	Operation	operator: 80 operands: 75
64	Literal
65	Literal
66	Operation	operator: 78 operands: 76
67	Operation	operator: 80 operands: 77
68	Operation	operator: 78 operands: 79
69	Operation	operator: 80 operands: 81
70	Literal
71	ExprTuple	82
72	Literal
73	Literal
74	NamedExprs	operation: 83 part: 86
75	ExprTuple	98, 88
76	NamedExprs	state: 84 part: 86
77	ExprTuple	98, 99
78	Literal
79	NamedExprs	state: 85 part: 86
80	Literal
81	ExprTuple	87, 88
82	Literal
83	Operation	operator: 89 operands: 90
84	Operation	operator: 91 operands: 92
85	Literal
86	Variable
87	Operation	operator: 94 operands: 93
88	Operation	operator: 94 operands: 95
89	Literal
90	ExprTuple	96, 99
91	Literal
92	ExprTuple	97, 99
93	ExprTuple	99, 98
94	Literal
95	ExprTuple	99, 100
96	Literal
97	Variable
98	Literal
99	Literal
100	Literal