Expression of type ExprTuple

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 Conditional, ExprTuple, Lambda, U, m
from proveit.linear_algebra import Unitary
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Exp, NaturalPos, one, two
from proveit.physics.quantum import m_ket_domain, var_ket_psi
from proveit.physics.quantum.circuits import unitary_gate_op
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(m, Conditional(Forall(instance_param_or_params = [U, var_ket_psi], instance_expr = Equals(Prob(unitary_gate_op), one), domains = [Unitary(Exp(two, m)), m_ket_domain]), InSet(m, NaturalPos))))

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\{\forall_{U \in \textrm{U}\left(2^{m}\right), \lvert \psi \rangle \in \mathbb{C}^{2^{m}}}~\left(\textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert \psi \rangle} & \gate{U} & \qout{U \thinspace \lvert \psi \rangle}
} \end{array}\right) = 1\right) \textrm{ if } m \in \mathbb{N}^+\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 72 body: 3
2	ExprTuple	72
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 24 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	72, 10
9	Lambda	parameters: 74 body: 11
10	Literal
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operands: 15
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18, 71
16	Literal
17	ExprTuple	19, 20
18	Operation	operator: 21 operand: 26
19	Operation	operator: 24 operands: 23
20	Operation	operator: 24 operands: 25
21	Literal
22	ExprTuple	26
23	ExprTuple	75, 27
24	Literal
25	ExprTuple	76, 28
26	Operation	operator: 29 operands: 30
27	Operation	operator: 31 operand: 39
28	Operation	operator: 33 operands: 34
29	Literal
30	ExprTuple	35, 36, 37
31	Literal
32	ExprTuple	39
33	Literal
34	ExprTuple	38, 39
35	ExprTuple	40
36	ExprTuple	41
37	ExprTuple	42
38	Literal
39	Operation	operator: 43 operands: 44
40	ExprRange	lambda_map: 45 start_index: 71 end_index: 72
41	ExprRange	lambda_map: 46 start_index: 71 end_index: 72
42	ExprRange	lambda_map: 47 start_index: 71 end_index: 72
43	Literal
44	ExprTuple	48, 72
45	Lambda	parameter: 70 body: 49
46	Lambda	parameter: 70 body: 50
47	Lambda	parameter: 70 body: 52
48	Literal
49	Operation	operator: 55 operands: 53
50	Operation	operator: 55 operands: 54
51	ExprTuple	70
52	Operation	operator: 55 operands: 56
53	NamedExprs	element: 57 targets: 60
54	NamedExprs	element: 58 targets: 60
55	Literal
56	NamedExprs	element: 59 targets: 60
57	Operation	operator: 61 operands: 62
58	Operation	operator: 63 operands: 64
59	Operation	operator: 65 operands: 66
60	Operation	operator: 67 operands: 68
61	Literal
62	NamedExprs	state: 76 part: 70
63	Literal
64	NamedExprs	operation: 75 part: 70
65	Literal
66	NamedExprs	state: 69 part: 70
67	Literal
68	ExprTuple	71, 72
69	Operation	operator: 73 operands: 74
70	Variable
71	Literal
72	Variable
73	Literal
74	ExprTuple	75, 76
75	Variable
76	Variable