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.logic import Equals
from proveit.physics.quantum.QPE import _Omega, _sample_space

# build up the expression from sub-expressions
expr = Equals(_Omega, _sample_space)

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())

\Omega = \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\}_{m \in \{0~\ldotp \ldotp~2^{t} - 1\}}

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	Literal
4	Operation	operator: 5 operand: 7
5	Literal
6	ExprTuple	7
7	Lambda	parameter: 101 body: 9
8	ExprTuple	101
9	Conditional	value: 10 condition: 11
10	Operation	operator: 12 operands: 13
11	Operation	operator: 14 operands: 15
12	Literal
13	ExprTuple	16, 17, 18, 19
14	Literal
15	ExprTuple	101, 20
16	ExprTuple	21, 22
17	ExprTuple	23, 24
18	ExprTuple	25, 26
19	ExprTuple	27, 28
20	Operation	operator: 83 operands: 29
21	ExprRange	lambda_map: 30 start_index: 102 end_index: 103
22	ExprRange	lambda_map: 31 start_index: 102 end_index: 104
23	ExprRange	lambda_map: 32 start_index: 102 end_index: 103
24	ExprRange	lambda_map: 32 start_index: 91 end_index: 92
25	ExprRange	lambda_map: 33 start_index: 102 end_index: 103
26	ExprRange	lambda_map: 34 start_index: 102 end_index: 104
27	ExprRange	lambda_map: 35 start_index: 102 end_index: 103
28	ExprRange	lambda_map: 36 start_index: 102 end_index: 104
29	ExprTuple	37, 38
30	Lambda	parameter: 90 body: 39
31	Lambda	parameter: 90 body: 40
32	Lambda	parameter: 90 body: 41
33	Lambda	parameter: 90 body: 42
34	Lambda	parameter: 90 body: 43
35	Lambda	parameter: 90 body: 44
36	Lambda	parameter: 90 body: 46
37	Literal
38	Operation	operator: 98 operands: 47
39	Operation	operator: 75 operands: 48
40	Operation	operator: 55 operands: 49
41	Operation	operator: 55 operands: 50
42	Operation	operator: 51 operands: 52
43	Operation	operator: 76 operands: 53
44	Operation	operator: 55 operands: 54
45	ExprTuple	90
46	Operation	operator: 55 operands: 56
47	ExprTuple	57, 58
48	NamedExprs	state: 59
49	NamedExprs	element: 60 targets: 68
50	NamedExprs	element: 61 targets: 62
51	Literal
52	NamedExprs	basis: 63
53	NamedExprs	operation: 64
54	NamedExprs	element: 65 targets: 66
55	Literal
56	NamedExprs	element: 67 targets: 68
57	Operation	operator: 69 operands: 70
58	Operation	operator: 71 operand: 102
59	Operation	operator: 73 operand: 86
60	Operation	operator: 75 operands: 82
61	Operation	operator: 76 operands: 77
62	Operation	operator: 83 operands: 78
63	Literal
64	Literal
65	Operation	operator: 81 operands: 79
66	Operation	operator: 83 operands: 80
67	Operation	operator: 81 operands: 82
68	Operation	operator: 83 operands: 84
69	Literal
70	ExprTuple	85, 103
71	Literal
72	ExprTuple	102
73	Literal
74	ExprTuple	86
75	Literal
76	Literal
77	NamedExprs	operation: 87 part: 90
78	ExprTuple	102, 92
79	NamedExprs	state: 88 part: 90
80	ExprTuple	102, 103
81	Literal
82	NamedExprs	state: 89 part: 90
83	Literal
84	ExprTuple	91, 92
85	Literal
86	Literal
87	Operation	operator: 93 operands: 94
88	Operation	operator: 95 operands: 96
89	Literal
90	Variable
91	Operation	operator: 98 operands: 97
92	Operation	operator: 98 operands: 99
93	Literal
94	ExprTuple	100, 103
95	Literal
96	ExprTuple	101, 103
97	ExprTuple	103, 102
98	Literal
99	ExprTuple	103, 104
100	Literal
101	Variable
102	Literal
103	Literal
104	Literal