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 A, Conditional, 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 = 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())

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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 53 body: 2
1	ExprTuple	53
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	53, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	51, 31
12	Operation	operator: 13 operands: 14
13	Literal
14	ExprTuple	15, 16
15	Operation	operator: 17 operands: 18
16	Operation	operator: 19 operands: 20
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	51, 23
21	Operation	operator: 25 operand: 29
22	Operation	operator: 25 operand: 30
23	Operation	operator: 27 operands: 28
24	ExprTuple	29
25	Literal
26	ExprTuple	30
27	Literal
28	ExprTuple	31
29	ExprTuple	32
30	ExprTuple	33
31	ExprRange	lambda_map: 34 start_index: 52 end_index: 53
32	ExprRange	lambda_map: 35 start_index: 52 end_index: 53
33	ExprRange	lambda_map: 36 start_index: 52 end_index: 53
34	Lambda	parameter: 54 body: 44
35	Lambda	parameter: 54 body: 37
36	Lambda	parameter: 54 body: 38
37	Operation	operator: 39 operands: 40
38	Operation	operator: 45 operands: 41
39	Literal
40	NamedExprs	element: 42 targets: 43
41	NamedExprs	state: 44
42	Operation	operator: 45 operands: 46
43	Operation	operator: 47 operands: 48
44	IndexedVar	variable: 49 index: 54
45	Literal
46	NamedExprs	state: 51 part: 54
47	Literal
48	ExprTuple	52, 53
49	Variable
50	ExprTuple	54
51	Variable
52	Literal
53	Variable
54	Variable