Expression of type Iff

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 A
from proveit.core_expr_types import B_1_to_m
from proveit.linear_algebra import TensorProd
from proveit.logic import Equals, Iff
from proveit.physics.quantum.circuits import QcircuitEquiv, circuit_compressed_inputAm, circuit_expanded_inputBm

# build up the expression from sub-expressions
expr = Iff(QcircuitEquiv(circuit_compressed_inputAm, circuit_expanded_inputBm), Equals(A, TensorProd(B_1_to_m)))

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(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{A} & { /^{m} } \qw
} \end{array}\right) \cong \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{B_{1}} & \qw \\
\qin{B_{2}} & \qw \\
\qin{\vdots} & \qw \\
\qin{B_{m}} & \qw
} \end{array}\right)\right) \Leftrightarrow \left(A = \left(B_{1} {\otimes}  B_{2} {\otimes}  \ldots {\otimes}  B_{m}\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	39, 11
9	Operation	operator: 13 operand: 17
10	Operation	operator: 13 operand: 18
11	Operation	operator: 15 operands: 16
12	ExprTuple	17
13	Literal
14	ExprTuple	18
15	Literal
16	ExprTuple	19
17	ExprTuple	20
18	ExprTuple	21
19	ExprRange	lambda_map: 22 start_index: 40 end_index: 41
20	ExprRange	lambda_map: 23 start_index: 40 end_index: 41
21	ExprRange	lambda_map: 24 start_index: 40 end_index: 41
22	Lambda	parameter: 42 body: 32
23	Lambda	parameter: 42 body: 25
24	Lambda	parameter: 42 body: 26
25	Operation	operator: 27 operands: 28
26	Operation	operator: 33 operands: 29
27	Literal
28	NamedExprs	element: 30 targets: 31
29	NamedExprs	state: 32
30	Operation	operator: 33 operands: 34
31	Operation	operator: 35 operands: 36
32	IndexedVar	variable: 37 index: 42
33	Literal
34	NamedExprs	state: 39 part: 42
35	Literal
36	ExprTuple	40, 41
37	Variable
38	ExprTuple	42
39	Variable
40	Literal
41	Variable
42	Variable