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 A, Conditional, ExprTuple, Lambda, m
from proveit.core_expr_types import B_1_to_m
from proveit.linear_algebra import TensorProd
from proveit.logic import Equals, Forall, Iff, InSet
from proveit.numbers import NaturalPos
from proveit.physics.quantum.circuits import QcircuitEquiv, circuit_compressed_inputAm, circuit_expanded_inputBm

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(m, Conditional(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)))), InSet(m, NaturalPos))))

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