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 ExprTuple, Lambda, m, n
from proveit.logic import Bijections, Forall, InSet, NotEquals, TRUE
from proveit.physics.quantum.QPE import _Omega, _m_domain, _phase_est_circuit

# build up the expression from sub-expressions
expr = ExprTuple(Forall(instance_param_or_params = [m, n], instance_expr = TRUE, domain = _m_domain, condition = NotEquals(m, n)), InSet(Lambda(m, _phase_est_circuit), Bijections(_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(\forall_{m, n \in \{0~\ldotp \ldotp~2^{t} - 1\}~|~m \neq n}~\top, \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] \in \left[\{0~\ldotp \ldotp~2^{t} - 1\} \xrightarrow[\text{onto}]{\text{1-to-1}} \Omega\right]\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 3 operand: 6
2	Operation	operator: 37 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameters: 40 body: 9
7	Lambda	parameter: 115 body: 11
8	Operation	operator: 12 operands: 13
9	Conditional	value: 14 condition: 15
10	ExprTuple	115
11	Operation	operator: 16 operands: 17
12	Literal
13	ExprTuple	48, 18
14	Literal
15	Operation	operator: 19 operands: 20
16	Literal
17	ExprTuple	21, 22, 23, 24
18	Literal
19	Literal
20	ExprTuple	25, 26, 27
21	ExprTuple	28, 29
22	ExprTuple	30, 31
23	ExprTuple	32, 33
24	ExprTuple	34, 35
25	Operation	operator: 37 operands: 36
26	Operation	operator: 37 operands: 38
27	Operation	operator: 39 operands: 40
28	ExprRange	lambda_map: 41 start_index: 116 end_index: 117
29	ExprRange	lambda_map: 42 start_index: 116 end_index: 118
30	ExprRange	lambda_map: 43 start_index: 116 end_index: 117
31	ExprRange	lambda_map: 43 start_index: 100 end_index: 101
32	ExprRange	lambda_map: 44 start_index: 116 end_index: 117
33	ExprRange	lambda_map: 45 start_index: 116 end_index: 118
34	ExprRange	lambda_map: 46 start_index: 116 end_index: 117
35	ExprRange	lambda_map: 47 start_index: 116 end_index: 118
36	ExprTuple	115, 48
37	Literal
38	ExprTuple	49, 48
39	Literal
40	ExprTuple	115, 49
41	Lambda	parameter: 99 body: 50
42	Lambda	parameter: 99 body: 51
43	Lambda	parameter: 99 body: 52
44	Lambda	parameter: 99 body: 53
45	Lambda	parameter: 99 body: 54
46	Lambda	parameter: 99 body: 55
47	Lambda	parameter: 99 body: 57
48	Operation	operator: 91 operands: 58
49	Variable
50	Operation	operator: 83 operands: 59
51	Operation	operator: 66 operands: 60
52	Operation	operator: 66 operands: 61
53	Operation	operator: 62 operands: 63
54	Operation	operator: 84 operands: 64
55	Operation	operator: 66 operands: 65
56	ExprTuple	99
57	Operation	operator: 66 operands: 67
58	ExprTuple	68, 69
59	NamedExprs	state: 70
60	NamedExprs	element: 71 targets: 79
61	NamedExprs	element: 72 targets: 73
62	Literal
63	NamedExprs	basis: 74
64	NamedExprs	operation: 75
65	NamedExprs	element: 76 targets: 77
66	Literal
67	NamedExprs	element: 78 targets: 79
68	Literal
69	Operation	operator: 111 operands: 80
70	Operation	operator: 81 operand: 95
71	Operation	operator: 83 operands: 90
72	Operation	operator: 84 operands: 85
73	Operation	operator: 91 operands: 86
74	Literal
75	Literal
76	Operation	operator: 89 operands: 87
77	Operation	operator: 91 operands: 88
78	Operation	operator: 89 operands: 90
79	Operation	operator: 91 operands: 92
80	ExprTuple	93, 94
81	Literal
82	ExprTuple	95
83	Literal
84	Literal
85	NamedExprs	operation: 96 part: 99
86	ExprTuple	116, 101
87	NamedExprs	state: 97 part: 99
88	ExprTuple	116, 117
89	Literal
90	NamedExprs	state: 98 part: 99
91	Literal
92	ExprTuple	100, 101
93	Operation	operator: 102 operands: 103
94	Operation	operator: 104 operand: 116
95	Literal
96	Operation	operator: 106 operands: 107
97	Operation	operator: 108 operands: 109
98	Literal
99	Variable
100	Operation	operator: 111 operands: 110
101	Operation	operator: 111 operands: 112
102	Literal
103	ExprTuple	113, 117
104	Literal
105	ExprTuple	116
106	Literal
107	ExprTuple	114, 117
108	Literal
109	ExprTuple	115, 117
110	ExprTuple	117, 116
111	Literal
112	ExprTuple	117, 118
113	Literal
114	Literal
115	Variable
116	Literal
117	Literal
118	Literal