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.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 = 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(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)

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