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, a, b, k, m
from proveit.core_expr_types import U_1_to_m
from proveit.logic import And, Forall, Implies, InSet
from proveit.numbers import NaturalPos
from proveit.physics.quantum.circuits import QcircuitEquiv, circuit_aU, circuit_aUb, circuit_b

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([k, m], Conditional(Forall(instance_param_or_params = [a, b, U_1_to_m], instance_expr = Implies(circuit_aUb, QcircuitEquiv(circuit_aU, circuit_b))), And(InSet(k, NaturalPos), 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(\left(k, m\right) \mapsto \left\{\forall_{a, b, U_{1}, U_{2}, \ldots, U_{m}}~\left(\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{a} & \gate{\begin{array}{c} \uparrow \\U_{1} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\U_{2} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\\cdots \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\U_{m} \\ \downarrow\end{array}} & \qout{b}
} \end{array}\right) \Rightarrow \left(\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{a} & \gate{\begin{array}{c} \uparrow \\U_{1} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\U_{2} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\\cdots \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\U_{m} \\ \downarrow\end{array}} & { /^{k} } \qw
} \end{array}\right) \cong \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{b} & { /^{k} } \qw
} \end{array}\right)\right)\right) \textrm{ if } k \in \mathbb{N}^+ ,  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	parameters: 2 body: 3
2	ExprTuple	67, 40
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	parameters: 13 body: 14
11	Operation	operator: 16 operands: 15
12	Operation	operator: 16 operands: 17
13	ExprTuple	63, 64, 35
14	Operation	operator: 18 operands: 19
15	ExprTuple	67, 20
16	Literal
17	ExprTuple	40, 20
18	Literal
19	ExprTuple	21, 22
20	Literal
21	Operation	operator: 31 operands: 23
22	Operation	operator: 24 operands: 25
23	ExprTuple	34, 35, 26
24	Literal
25	ExprTuple	27, 28
26	ExprTuple	29
27	Operation	operator: 31 operands: 30
28	Operation	operator: 31 operand: 36
29	ExprRange	lambda_map: 33 start_index: 66 end_index: 67
30	ExprTuple	34, 35
31	Literal
32	ExprTuple	36
33	Lambda	parameter: 65 body: 37
34	ExprTuple	38
35	ExprRange	lambda_map: 39 start_index: 66 end_index: 40
36	ExprTuple	41
37	Operation	operator: 53 operands: 42
38	ExprRange	lambda_map: 43 start_index: 66 end_index: 67
39	Lambda	parameter: 65 body: 44
40	Variable
41	ExprRange	lambda_map: 45 start_index: 66 end_index: 67
42	NamedExprs	element: 46 targets: 57
43	Lambda	parameter: 65 body: 47
44	IndexedVar	variable: 48 index: 65
45	Lambda	parameter: 65 body: 50
46	Operation	operator: 51 operands: 60
47	Operation	operator: 53 operands: 52
48	Variable
49	ExprTuple	65
50	Operation	operator: 53 operands: 54
51	Literal
52	NamedExprs	element: 55 targets: 57
53	Literal
54	NamedExprs	element: 56 targets: 57
55	Operation	operator: 59 operands: 58
56	Operation	operator: 59 operands: 60
57	Operation	operator: 61 operands: 62
58	NamedExprs	state: 63 part: 65
59	Literal
60	NamedExprs	state: 64 part: 65
61	Literal
62	ExprTuple	66, 67
63	Variable
64	Variable
65	Variable
66	Literal
67	Variable