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

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, b, U_1_to_m], instance_expr = 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())

\forall_{a, b, U_{1}, U_{2}, \ldots, U_{m}}~\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)

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