Expression of type Forall

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 m
from proveit.logic import Equals, Forall
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 = Forall(instance_param_or_params = [m], instance_expr = Equals(Prob(_phase_est_circuit), _alpha_m_sqrd), domain = _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())

\forall_{m \in \{0~\ldotp \ldotp~2^{t} - 1\}}~\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}\right)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameter: 110 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	110, 13
11	Operation	operator: 14 operand: 18
12	Operation	operator: 44 operands: 16
13	Operation	operator: 93 operands: 17
14	Literal
15	ExprTuple	18
16	ExprTuple	19, 55
17	ExprTuple	20, 21
18	Operation	operator: 22 operands: 23
19	Operation	operator: 24 operand: 31
20	Literal
21	Operation	operator: 107 operands: 26
22	Literal
23	ExprTuple	27, 28, 29, 30
24	Literal
25	ExprTuple	31
26	ExprTuple	32, 33
27	ExprTuple	34, 35
28	ExprTuple	36, 37
29	ExprTuple	38, 39
30	ExprTuple	40, 41
31	Operation	operator: 42 operand: 110
32	Operation	operator: 44 operands: 45
33	Operation	operator: 46 operand: 111
34	ExprRange	lambda_map: 48 start_index: 111 end_index: 112
35	ExprRange	lambda_map: 49 start_index: 111 end_index: 113
36	ExprRange	lambda_map: 50 start_index: 111 end_index: 112
37	ExprRange	lambda_map: 50 start_index: 100 end_index: 101
38	ExprRange	lambda_map: 51 start_index: 111 end_index: 112
39	ExprRange	lambda_map: 52 start_index: 111 end_index: 113
40	ExprRange	lambda_map: 53 start_index: 111 end_index: 112
41	ExprRange	lambda_map: 54 start_index: 111 end_index: 113
42	Literal
43	ExprTuple	110
44	Literal
45	ExprTuple	55, 112
46	Literal
47	ExprTuple	111
48	Lambda	parameter: 99 body: 56
49	Lambda	parameter: 99 body: 57
50	Lambda	parameter: 99 body: 58
51	Lambda	parameter: 99 body: 59
52	Lambda	parameter: 99 body: 60
53	Lambda	parameter: 99 body: 61
54	Lambda	parameter: 99 body: 63
55	Literal
56	Operation	operator: 85 operands: 64
57	Operation	operator: 71 operands: 65
58	Operation	operator: 71 operands: 66
59	Operation	operator: 67 operands: 68
60	Operation	operator: 86 operands: 69
61	Operation	operator: 71 operands: 70
62	ExprTuple	99
63	Operation	operator: 71 operands: 72
64	NamedExprs	state: 73
65	NamedExprs	element: 74 targets: 82
66	NamedExprs	element: 75 targets: 76
67	Literal
68	NamedExprs	basis: 77
69	NamedExprs	operation: 78
70	NamedExprs	element: 79 targets: 80
71	Literal
72	NamedExprs	element: 81 targets: 82
73	Operation	operator: 83 operand: 95
74	Operation	operator: 85 operands: 92
75	Operation	operator: 86 operands: 87
76	Operation	operator: 93 operands: 88
77	Literal
78	Literal
79	Operation	operator: 91 operands: 89
80	Operation	operator: 93 operands: 90
81	Operation	operator: 91 operands: 92
82	Operation	operator: 93 operands: 94
83	Literal
84	ExprTuple	95
85	Literal
86	Literal
87	NamedExprs	operation: 96 part: 99
88	ExprTuple	111, 101
89	NamedExprs	state: 97 part: 99
90	ExprTuple	111, 112
91	Literal
92	NamedExprs	state: 98 part: 99
93	Literal
94	ExprTuple	100, 101
95	Literal
96	Operation	operator: 102 operands: 103
97	Operation	operator: 104 operands: 105
98	Literal
99	Variable
100	Operation	operator: 107 operands: 106
101	Operation	operator: 107 operands: 108
102	Literal
103	ExprTuple	109, 112
104	Literal
105	ExprTuple	110, 112
106	ExprTuple	112, 111
107	Literal
108	ExprTuple	112, 113
109	Literal
110	Variable
111	Literal
112	Literal
113	Literal