Theorem input_as_tensor_prod of type Forall

from the theory of proveit.physics.quantum.circuits

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.physics.quantum.circuits import input_as_tensor_prod

# check that the built expression is the same as the stored expression
assert input_as_tensor_prod.expr == stored_expr
assert input_as_tensor_prod.expr._style_id == stored_expr._style_id
print("Passed sanity check: input_as_tensor_prod matches stored_expr")

Passed sanity check: input_as_tensor_prod matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{m \in \mathbb{N}^+}~\left[\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)\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: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 55 body: 4
3	ExprTuple	55
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 11
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11
9	Literal
10	ExprTuple	55, 12
11	Lambda	parameters: 13 body: 14
12	Literal
13	ExprTuple	53, 33
14	Operation	operator: 15 operands: 16
15	Literal
16	ExprTuple	17, 18
17	Operation	operator: 19 operands: 20
18	Operation	operator: 21 operands: 22
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	53, 25
23	Operation	operator: 27 operand: 31
24	Operation	operator: 27 operand: 32
25	Operation	operator: 29 operands: 30
26	ExprTuple	31
27	Literal
28	ExprTuple	32
29	Literal
30	ExprTuple	33
31	ExprTuple	34
32	ExprTuple	35
33	ExprRange	lambda_map: 36 start_index: 54 end_index: 55
34	ExprRange	lambda_map: 37 start_index: 54 end_index: 55
35	ExprRange	lambda_map: 38 start_index: 54 end_index: 55
36	Lambda	parameter: 56 body: 46
37	Lambda	parameter: 56 body: 39
38	Lambda	parameter: 56 body: 40
39	Operation	operator: 41 operands: 42
40	Operation	operator: 47 operands: 43
41	Literal
42	NamedExprs	element: 44 targets: 45
43	NamedExprs	state: 46
44	Operation	operator: 47 operands: 48
45	Operation	operator: 49 operands: 50
46	IndexedVar	variable: 51 index: 56
47	Literal
48	NamedExprs	state: 53 part: 56
49	Literal
50	ExprTuple	54, 55
51	Variable
52	ExprTuple	56
53	Variable
54	Literal
55	Variable
56	Variable