Expression of type Forall

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, Forall, Iff
from proveit.physics.quantum.circuits import QcircuitEquiv, circuit_compressed_inputAm, circuit_expanded_inputBm

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [A, B_1_to_m], instance_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())

\forall_{A, B_{1}, B_{2}, \ldots, B_{m}}~\left(\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)\right)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 4 body: 5
4	ExprTuple	44, 24
5	Operation	operator: 6 operands: 7
6	Literal
7	ExprTuple	8, 9
8	Operation	operator: 10 operands: 11
9	Operation	operator: 12 operands: 13
10	Literal
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	44, 16
14	Operation	operator: 18 operand: 22
15	Operation	operator: 18 operand: 23
16	Operation	operator: 20 operands: 21
17	ExprTuple	22
18	Literal
19	ExprTuple	23
20	Literal
21	ExprTuple	24
22	ExprTuple	25
23	ExprTuple	26
24	ExprRange	lambda_map: 27 start_index: 45 end_index: 46
25	ExprRange	lambda_map: 28 start_index: 45 end_index: 46
26	ExprRange	lambda_map: 29 start_index: 45 end_index: 46
27	Lambda	parameter: 47 body: 37
28	Lambda	parameter: 47 body: 30
29	Lambda	parameter: 47 body: 31
30	Operation	operator: 32 operands: 33
31	Operation	operator: 38 operands: 34
32	Literal
33	NamedExprs	element: 35 targets: 36
34	NamedExprs	state: 37
35	Operation	operator: 38 operands: 39
36	Operation	operator: 40 operands: 41
37	IndexedVar	variable: 42 index: 47
38	Literal
39	NamedExprs	state: 44 part: 47
40	Literal
41	ExprTuple	45, 46
42	Variable
43	ExprTuple	47
44	Variable
45	Literal
46	Variable
47	Variable