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 Conditional, ExprRange, ExprTuple, Lambda, U, Variable, VertExprArray, s, t
from proveit.linear_algebra import Unitary
from proveit.logic import And, Forall, InSet
from proveit.numbers import Add, Exp, Interval, NaturalPos, one, two
from proveit.physics.quantum.QPE import QPE1, QPE1_U_t_circuit
from proveit.physics.quantum.circuits import Gate, MultiQubitElem, Qcircuit, QcircuitEquiv

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(t, s)
sub_expr3 = MultiQubitElem(element = Gate(operation = QPE1(U, t), part = sub_expr1), targets = Interval(one, sub_expr2))
expr = ExprTuple(Lambda([s, t], Conditional(Forall(instance_param_or_params = [U], instance_expr = QcircuitEquiv(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, sub_expr3, one, t), ExprRange(sub_expr1, sub_expr3, Add(t, one), sub_expr2)])), QPE1_U_t_circuit), domain = Unitary(Exp(two, s))), And(InSet(s, NaturalPos), InSet(t, 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(\left(s, t\right) \mapsto \left\{\forall_{U \in \textrm{U}\left(2^{s}\right)}~\left(\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \multigate{1}{\textrm{QPE}_1\left(U, t\right)} & { /^{t} } \qw \\
& \ghost{\textrm{QPE}_1\left(U, t\right)} & { /^{s} } \qw
} \end{array}\right) \cong \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \control{} \qw \qwx[1] & \qw & \gate{\cdots} \qwx[1] & \qw & \qw \\
& \qw \qwx[1] & \control{} \qw \qwx[1] & \gate{\cdots} \qwx[1] & \qw & \qw \\
& \gate{\vdots} \qwx[1] & \gate{\vdots} \qwx[1] & \gate{\ddots} \qwx[1] & \gate{\vdots} & \qw \\
& \qw \qwx[1] & \qw \qwx[1] & \gate{\cdots} \qwx[1] & \control{} \qw \qwx[1] & \qw \\
& \gate{U^{2^{t - 1}}} & \gate{U^{2^{t - 2}}} & \gate{\cdots} & \gate{U^{2^{0}}} & { /^{s} } \qw
} \end{array}\right)\right) \textrm{ if } s \in \mathbb{N}^+ ,  t \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	parameters: 2 body: 3
2	ExprTuple	98, 106
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	11, 12
10	Lambda	parameter: 96 body: 14
11	Operation	operator: 22 operands: 15
12	Operation	operator: 22 operands: 16
13	ExprTuple	96
14	Conditional	value: 17 condition: 18
15	ExprTuple	98, 19
16	ExprTuple	106, 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	Literal
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	96, 26
24	Operation	operator: 28 operand: 32
25	Operation	operator: 28 operands: 29
26	Operation	operator: 30 operand: 34
27	ExprTuple	32
28	Literal
29	ExprTuple	33
30	Literal
31	ExprTuple	34
32	ExprTuple	35, 36
33	ExprRange	lambda_map: 37 start_index: 38 end_index: 39
34	Operation	operator: 100 operands: 40
35	ExprRange	lambda_map: 41 start_index: 107 end_index: 106
36	ExprRange	lambda_map: 41 start_index: 99 end_index: 84
37	Lambda	parameter: 110 body: 42
38	Operation	operator: 102 operands: 43
39	Literal
40	ExprTuple	104, 98
41	Lambda	parameter: 89 body: 44
42	ExprTuple	45, 46
43	ExprTuple	47, 107
44	Operation	operator: 76 operands: 48
45	ExprRange	lambda_map: 49 start_index: 107 end_index: 106
46	ExprRange	lambda_map: 50 start_index: 107 end_index: 98
47	Operation	operator: 108 operand: 106
48	NamedExprs	element: 52 targets: 53
49	Lambda	parameter: 89 body: 54
50	Lambda	parameter: 89 body: 56
51	ExprTuple	106
52	Operation	operator: 79 operands: 57
53	Operation	operator: 74 operands: 58
54	Operation	operator: 59 operands: 60
55	ExprTuple	89
56	Operation	operator: 76 operands: 61
57	NamedExprs	operation: 62 part: 89
58	ExprTuple	107, 84
59	Literal
60	ExprTuple	63, 64
61	NamedExprs	element: 65 targets: 66
62	Operation	operator: 67 operands: 68
63	Conditional	value: 69 condition: 70
64	Conditional	value: 71 condition: 72
65	Operation	operator: 79 operands: 73
66	Operation	operator: 74 operands: 75
67	Literal
68	ExprTuple	96, 106
69	Operation	operator: 76 operands: 77
70	Operation	operator: 78 operands: 82
71	Operation	operator: 79 operands: 80
72	Operation	operator: 81 operands: 82
73	NamedExprs	operation: 83 part: 89
74	Literal
75	ExprTuple	99, 84
76	Literal
77	NamedExprs	element: 85 targets: 86
78	Literal
79	Literal
80	NamedExprs	operation: 87
81	Literal
82	ExprTuple	88, 89
83	Operation	operator: 90 operands: 91
84	Operation	operator: 102 operands: 92
85	Literal
86	Operation	operator: 93 operand: 99
87	Literal
88	Operation	operator: 102 operands: 95
89	Variable
90	Literal
91	ExprTuple	96, 97
92	ExprTuple	106, 98
93	Literal
94	ExprTuple	99
95	ExprTuple	110, 106
96	Variable
97	Operation	operator: 100 operands: 101
98	Variable
99	Operation	operator: 102 operands: 103
100	Literal
101	ExprTuple	104, 105
102	Literal
103	ExprTuple	106, 107
104	Literal
105	Operation	operator: 108 operand: 110
106	Variable
107	Literal
108	Literal
109	ExprTuple	110
110	Variable