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 ExprTuple, Lambda
from proveit.core_expr_types.expr_arrays import A11_to_Akl, A11_to_Akl_varray, B11_to_Bkl, B11_to_Bkl_varray
from proveit.logic import Implies, NotEquals
from proveit.physics.quantum.circuits import circuit_Akl, circuit_Bkl

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([A11_to_Akl, B11_to_Bkl], Implies(NotEquals(A11_to_Akl_varray, B11_to_Bkl_varray), NotEquals(circuit_Akl, circuit_Bkl)).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(\left(A_{1, 1}, A_{1, 2}, \ldots, A_{1, l}, A_{2, 1}, A_{2, 2}, \ldots, A_{2, l}, \ldots\ldots, A_{k, 1}, A_{k, 2}, \ldots, A_{k, l}, B_{1, 1}, B_{1, 2}, \ldots, B_{1, l}, B_{2, 1}, B_{2, 2}, \ldots, B_{2, l}, \ldots\ldots, B_{k, 1}, B_{k, 2}, \ldots, B_{k, l}\right) \mapsto \left(\begin{array}{c} \begin{array}{l} \left(\left(\begin{array}{cccc} 
 A_{1, 1} & A_{2, 1} & \cdots & A_{k, 1} \\
A_{1, 2} & A_{2, 2} & \cdots & A_{k, 2} \\
\vdots & \vdots & \ddots & \vdots \\
A_{1, l} & A_{2, l} & \cdots & A_{k, l} \\
\end{array}
\right) \neq \left(\begin{array}{cccc} 
 B_{1, 1} & B_{2, 1} & \cdots & B_{k, 1} \\
B_{1, 2} & B_{2, 2} & \cdots & B_{k, 2} \\
\vdots & \vdots & \ddots & \vdots \\
B_{1, l} & B_{2, l} & \cdots & B_{k, l} \\
\end{array}
\right)\right) \Rightarrow  \\ \left(\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \gate{A_{1, 1}} \qwx[1] & \gate{A_{2, 1}} \qwx[1] & \gate{\cdots} \qwx[1] & \gate{A_{k, 1}} \qwx[1] & \qw \\
& \gate{A_{1, 2}} \qwx[1] & \gate{A_{2, 2}} \qwx[1] & \gate{\cdots} \qwx[1] & \gate{A_{k, 2}} \qwx[1] & \qw \\
& \gate{\vdots} \qwx[1] & \gate{\vdots} \qwx[1] & \gate{\ddots} \qwx[1] & \gate{\vdots} \qwx[1] & \qw \\
& \gate{A_{1, l}} & \gate{A_{2, l}} & \gate{\cdots} & \gate{A_{k, l}} & \qw
} \end{array}\right) \neq \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \gate{B_{1, 1}} \qwx[1] & \gate{B_{2, 1}} \qwx[1] & \gate{\cdots} \qwx[1] & \gate{B_{k, 1}} \qwx[1] & \qw \\
& \gate{B_{1, 2}} \qwx[1] & \gate{B_{2, 2}} \qwx[1] & \gate{\cdots} \qwx[1] & \gate{B_{k, 2}} \qwx[1] & \qw \\
& \gate{\vdots} \qwx[1] & \gate{\vdots} \qwx[1] & \gate{\ddots} \qwx[1] & \gate{\vdots} \qwx[1] & \qw \\
& \gate{B_{1, l}} & \gate{B_{2, l}} & \gate{\cdots} & \gate{B_{k, l}} & \qw
} \end{array}\right)\right) \end{array} \end{array}\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	4, 5
3	Operation	operator: 6 operands: 7
4	ExprRange	lambda_map: 8 start_index: 32 end_index: 24
5	ExprRange	lambda_map: 9 start_index: 32 end_index: 24
6	Literal
7	ExprTuple	10, 11
8	Lambda	parameter: 40 body: 28
9	Lambda	parameter: 40 body: 29
10	Operation	operator: 13 operands: 12
11	Operation	operator: 13 operands: 14
12	ExprTuple	17, 19
13	Literal
14	ExprTuple	15, 16
15	Operation	operator: 18 operands: 17
16	Operation	operator: 18 operands: 19
17	ExprTuple	20
18	Literal
19	ExprTuple	21
20	ExprRange	lambda_map: 22 start_index: 32 end_index: 24
21	ExprRange	lambda_map: 23 start_index: 32 end_index: 24
22	Lambda	parameter: 40 body: 25
23	Lambda	parameter: 40 body: 27
24	Variable
25	ExprTuple	28
26	ExprTuple	40
27	ExprTuple	29
28	ExprRange	lambda_map: 30 start_index: 32 end_index: 33
29	ExprRange	lambda_map: 31 start_index: 32 end_index: 33
30	Lambda	parameter: 41 body: 34
31	Lambda	parameter: 41 body: 36
32	Literal
33	Variable
34	IndexedVar	variable: 37 indices: 39
35	ExprTuple	41
36	IndexedVar	variable: 38 indices: 39
37	Variable
38	Variable
39	ExprTuple	40, 41
40	Variable
41	Variable