Expression of type Lambda

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 Lambda
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 Implies
from proveit.physics.quantum.circuits import QcircuitEquiv, circuit_AjBkCl, circuit_AjDmCl, circuit_Bk, circuit_Dm

# build up the expression from sub-expressions
expr = Lambda([A_1_to_j, B_1_to_k, C_1_to_l, D_1_to_m], Implies(QcircuitEquiv(circuit_Bk, circuit_Dm), QcircuitEquiv(circuit_AjBkCl, circuit_AjDmCl).with_wrapping_at(1)).with_wrapping_at(2))

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(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}\right) \mapsto \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)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	20, 19, 22, 21
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Operation	operator: 8 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13
10	Operation	operator: 17 operands: 14
11	Operation	operator: 17 operands: 15
12	Operation	operator: 17 operands: 16
13	Operation	operator: 17 operands: 18
14	ExprTuple	19
15	ExprTuple	21
16	ExprTuple	20, 19, 22
17	Literal
18	ExprTuple	20, 21, 22
19	ExprRange	lambda_map: 23 start_index: 30 end_index: 24
20	ExprRange	lambda_map: 25 start_index: 30 end_index: 26
21	ExprRange	lambda_map: 27 start_index: 30 end_index: 28
22	ExprRange	lambda_map: 29 start_index: 30 end_index: 31
23	Lambda	parameter: 41 body: 32
24	Variable
25	Lambda	parameter: 41 body: 33
26	Variable
27	Lambda	parameter: 41 body: 34
28	Variable
29	Lambda	parameter: 41 body: 35
30	Literal
31	Variable
32	IndexedVar	variable: 36 index: 41
33	IndexedVar	variable: 37 index: 41
34	IndexedVar	variable: 38 index: 41
35	IndexedVar	variable: 39 index: 41
36	Variable
37	Variable
38	Variable
39	Variable
40	ExprTuple	41
41	Variable