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, j, k, l, m
from proveit.core_expr_types import A_1_to_j, B_1_to_k, C_1_to_l, D_1_to_m
from proveit.logic import And, Forall, Implies, InSet
from proveit.numbers import Natural
from proveit.physics.quantum.circuits import QcircuitEquiv, circuit_AjBkCl, circuit_AjDmCl, circuit_Bk, circuit_Dm

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([j, k, l, m], Conditional(Forall(instance_param_or_params = [A_1_to_j, B_1_to_k, C_1_to_l, D_1_to_m], instance_expr = Implies(QcircuitEquiv(circuit_Bk, circuit_Dm), QcircuitEquiv(circuit_AjBkCl, circuit_AjDmCl).with_wrapping_at(1)).with_wrapping_at(2)).with_wrapping(), And(InSet(j, Natural), InSet(k, Natural), InSet(l, Natural), InSet(m, Natural)))))

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(j, k, l, m\right) \mapsto \left\{\begin{array}{l}\forall_{A_{1}, A_{2}, \ldots, A_{j}, B_{1}, B_{2}, \ldots, B_{k}, C_{1}, C_{2}, \ldots, C_{l}, D_{1}, D_{2}, \ldots, D_{m}}~\\
\left(\begin{array}{c} \begin{array}{l} \left(\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \gate{\begin{array}{c} \uparrow \\B_{1} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\B_{2} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\\cdots \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\B_{k} \\ \downarrow\end{array}} & \qw
} \end{array}\right) \cong \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \gate{\begin{array}{c} \uparrow \\D_{1} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\D_{2} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\\cdots \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\D_{m} \\ \downarrow\end{array}} & \qw
} \end{array}\right)\right) \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \gate{\begin{array}{c} \uparrow \\A_{1} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\A_{2} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\\cdots \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\A_{j} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\B_{1} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\B_{2} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\\cdots \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\B_{k} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\C_{1} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\C_{2} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\\cdots \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\C_{l} \\ \downarrow\end{array}} & \qw
} \end{array}\right) \\  \cong \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \gate{\begin{array}{c} \uparrow \\A_{1} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\A_{2} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\\cdots \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\A_{j} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\D_{1} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\D_{2} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\\cdots \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\D_{m} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\C_{1} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\C_{2} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\\cdots \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\C_{l} \\ \downarrow\end{array}} & \qw
} \end{array}\right) \end{array} \end{array}\right) \end{array} \end{array}\right)\end{array} \textrm{ if } j \in \mathbb{N} ,  k \in \mathbb{N} ,  l \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	46, 44, 51, 48
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, 13, 14
10	Lambda	parameters: 15 body: 16
11	Operation	operator: 20 operands: 17
12	Operation	operator: 20 operands: 18
13	Operation	operator: 20 operands: 19
14	Operation	operator: 20 operands: 21
15	ExprTuple	40, 39, 42, 41
16	Operation	operator: 22 operands: 23
17	ExprTuple	46, 24
18	ExprTuple	44, 24
19	ExprTuple	51, 24
20	Literal
21	ExprTuple	48, 24
22	Literal
23	ExprTuple	25, 26
24	Literal
25	Operation	operator: 28 operands: 27
26	Operation	operator: 28 operands: 29
27	ExprTuple	30, 31
28	Literal
29	ExprTuple	32, 33
30	Operation	operator: 37 operands: 34
31	Operation	operator: 37 operands: 35
32	Operation	operator: 37 operands: 36
33	Operation	operator: 37 operands: 38
34	ExprTuple	39
35	ExprTuple	41
36	ExprTuple	40, 39, 42
37	Literal
38	ExprTuple	40, 41, 42
39	ExprRange	lambda_map: 43 start_index: 50 end_index: 44
40	ExprRange	lambda_map: 45 start_index: 50 end_index: 46
41	ExprRange	lambda_map: 47 start_index: 50 end_index: 48
42	ExprRange	lambda_map: 49 start_index: 50 end_index: 51
43	Lambda	parameter: 61 body: 52
44	Variable
45	Lambda	parameter: 61 body: 53
46	Variable
47	Lambda	parameter: 61 body: 54
48	Variable
49	Lambda	parameter: 61 body: 55
50	Literal
51	Variable
52	IndexedVar	variable: 56 index: 61
53	IndexedVar	variable: 57 index: 61
54	IndexedVar	variable: 58 index: 61
55	IndexedVar	variable: 59 index: 61
56	Variable
57	Variable
58	Variable
59	Variable
60	ExprTuple	61
61	Variable