Expression of type Forall

from the theory of proveit.physics.quantum.circuits

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, n
from proveit.logic import Forall, InClass, SetOfAll
from proveit.numbers import NaturalPos
from proveit.physics.quantum import m_bit_interval, m_ket_domain, normalized_var_ket_psi, var_ket_psi
from proveit.physics.quantum.circuits import register_meas
from proveit.statistics import SampleSpaces

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [m, var_ket_psi], instance_expr = InClass(SetOfAll(instance_param_or_params = [n], instance_element = register_meas, domain = m_bit_interval), SampleSpaces), domains = [NaturalPos, m_ket_domain], condition = normalized_var_ket_psi)

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 \mathbb{N}^+, \lvert \psi \rangle \in \mathbb{C}^{2^{m}}~|~\left \|\lvert \psi \rangle\right \| = 1}~\left(\left\{\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\multiqin{3}{\lvert \psi \rangle} & \meter & \multiqout{3}{\lvert n \rangle_{m}} \\
\ghostqin{\lvert \psi \rangle} & \meter & \ghostqout{\lvert n \rangle_{m}} \\
\ghostqin{\lvert \psi \rangle} & \measure{\begin{array}{c}:\\ \left(m - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert n \rangle_{m}} \\
\ghostqin{\lvert \psi \rangle} & \meter & \ghostqout{\lvert n \rangle_{m}}
} \end{array}\right\}_{n \in \{0~\ldotp \ldotp~2^{m} - 1\}} \underset{{\scriptscriptstyle c}}{\in} \textrm{SampleSpaces}\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	parameters: 4 body: 5
4	ExprTuple	88, 81
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	14, 15, 16
12	Operation	operator: 17 operand: 23
13	Literal
14	Operation	operator: 38 operands: 19
15	Operation	operator: 38 operands: 20
16	Operation	operator: 21 operands: 22
17	Literal
18	ExprTuple	23
19	ExprTuple	88, 24
20	ExprTuple	81, 25
21	Literal
22	ExprTuple	26, 84
23	Lambda	parameter: 87 body: 28
24	Literal
25	Operation	operator: 29 operands: 30
26	Operation	operator: 31 operand: 81
27	ExprTuple	87
28	Conditional	value: 33 condition: 34
29	Literal
30	ExprTuple	35, 64
31	Literal
32	ExprTuple	81
33	Operation	operator: 36 operands: 37
34	Operation	operator: 38 operands: 39
35	Literal
36	Literal
37	ExprTuple	40, 41, 42
38	Literal
39	ExprTuple	87, 43
40	ExprTuple	44
41	ExprTuple	45
42	ExprTuple	46
43	Operation	operator: 78 operands: 47
44	ExprRange	lambda_map: 48 start_index: 84 end_index: 88
45	ExprRange	lambda_map: 49 start_index: 84 end_index: 88
46	ExprRange	lambda_map: 50 start_index: 84 end_index: 88
47	ExprTuple	51, 52
48	Lambda	parameter: 83 body: 53
49	Lambda	parameter: 83 body: 54
50	Lambda	parameter: 83 body: 56
51	Literal
52	Operation	operator: 57 operands: 58
53	Operation	operator: 62 operands: 59
54	Operation	operator: 60 operands: 61
55	ExprTuple	83
56	Operation	operator: 62 operands: 63
57	Literal
58	ExprTuple	64, 65
59	NamedExprs	element: 66 targets: 69
60	Literal
61	NamedExprs	basis: 67
62	Literal
63	NamedExprs	element: 68 targets: 69
64	Operation	operator: 70 operands: 71
65	Operation	operator: 72 operand: 84
66	Operation	operator: 74 operands: 75
67	Literal
68	Operation	operator: 76 operands: 77
69	Operation	operator: 78 operands: 79
70	Literal
71	ExprTuple	80, 88
72	Literal
73	ExprTuple	84
74	Literal
75	NamedExprs	state: 81 part: 83
76	Literal
77	NamedExprs	state: 82 part: 83
78	Literal
79	ExprTuple	84, 88
80	Literal
81	Variable
82	Operation	operator: 85 operands: 86
83	Variable
84	Literal
85	Literal
86	ExprTuple	87, 88
87	Variable
88	Variable