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 ExprTuple, Lambda, a, b
from proveit.core_expr_types import U_1_to_m
from proveit.logic import Implies
from proveit.physics.quantum.circuits import QcircuitEquiv, circuit_aU, circuit_aUb, circuit_b

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a, b, U_1_to_m], Implies(circuit_aUb, QcircuitEquiv(circuit_aU, circuit_b))))

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(a, b, U_{1}, U_{2}, \ldots, U_{m}\right) \mapsto \left(\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{a} & \gate{\begin{array}{c} \uparrow \\U_{1} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\U_{2} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\\cdots \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\U_{m} \\ \downarrow\end{array}} & \qout{b}
} \end{array}\right) \Rightarrow \left(\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{a} & \gate{\begin{array}{c} \uparrow \\U_{1} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\U_{2} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\\cdots \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\U_{m} \\ \downarrow\end{array}} & { /^{k} } \qw
} \end{array}\right) \cong \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{b} & { /^{k} } \qw
} \end{array}\right)\right)\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	parameters: 2 body: 3
2	ExprTuple	48, 49, 20
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 16 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	19, 20, 11
9	Literal
10	ExprTuple	12, 13
11	ExprTuple	14
12	Operation	operator: 16 operands: 15
13	Operation	operator: 16 operand: 21
14	ExprRange	lambda_map: 18 start_index: 51 end_index: 52
15	ExprTuple	19, 20
16	Literal
17	ExprTuple	21
18	Lambda	parameter: 50 body: 22
19	ExprTuple	23
20	ExprRange	lambda_map: 24 start_index: 51 end_index: 25
21	ExprTuple	26
22	Operation	operator: 38 operands: 27
23	ExprRange	lambda_map: 28 start_index: 51 end_index: 52
24	Lambda	parameter: 50 body: 29
25	Variable
26	ExprRange	lambda_map: 30 start_index: 51 end_index: 52
27	NamedExprs	element: 31 targets: 42
28	Lambda	parameter: 50 body: 32
29	IndexedVar	variable: 33 index: 50
30	Lambda	parameter: 50 body: 35
31	Operation	operator: 36 operands: 45
32	Operation	operator: 38 operands: 37
33	Variable
34	ExprTuple	50
35	Operation	operator: 38 operands: 39
36	Literal
37	NamedExprs	element: 40 targets: 42
38	Literal
39	NamedExprs	element: 41 targets: 42
40	Operation	operator: 44 operands: 43
41	Operation	operator: 44 operands: 45
42	Operation	operator: 46 operands: 47
43	NamedExprs	state: 48 part: 50
44	Literal
45	NamedExprs	state: 49 part: 50
46	Literal
47	ExprTuple	51, 52
48	Variable
49	Variable
50	Variable
51	Literal
52	Variable