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 U, m
from proveit.linear_algebra import Unitary
from proveit.logic import Equals, Forall
from proveit.numbers import Exp, one, two
from proveit.physics.quantum import m_ket_domain, var_ket_psi
from proveit.physics.quantum.circuits import unitary_gate_op
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [U, var_ket_psi], instance_expr = Equals(Prob(unitary_gate_op), one), domains = [Unitary(Exp(two, m)), m_ket_domain])

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_{U \in \textrm{U}\left(2^{m}\right), \lvert \psi \rangle \in \mathbb{C}^{2^{m}}}~\left(\textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert \psi \rangle} & \gate{U} & \qout{U \thinspace \lvert \psi \rangle}
} \end{array}\right) = 1\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: 67 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11, 64
9	Literal
10	ExprTuple	12, 13
11	Operation	operator: 14 operand: 19
12	Operation	operator: 17 operands: 16
13	Operation	operator: 17 operands: 18
14	Literal
15	ExprTuple	19
16	ExprTuple	68, 20
17	Literal
18	ExprTuple	69, 21
19	Operation	operator: 22 operands: 23
20	Operation	operator: 24 operand: 32
21	Operation	operator: 26 operands: 27
22	Literal
23	ExprTuple	28, 29, 30
24	Literal
25	ExprTuple	32
26	Literal
27	ExprTuple	31, 32
28	ExprTuple	33
29	ExprTuple	34
30	ExprTuple	35
31	Literal
32	Operation	operator: 36 operands: 37
33	ExprRange	lambda_map: 38 start_index: 64 end_index: 65
34	ExprRange	lambda_map: 39 start_index: 64 end_index: 65
35	ExprRange	lambda_map: 40 start_index: 64 end_index: 65
36	Literal
37	ExprTuple	41, 65
38	Lambda	parameter: 63 body: 42
39	Lambda	parameter: 63 body: 43
40	Lambda	parameter: 63 body: 45
41	Literal
42	Operation	operator: 48 operands: 46
43	Operation	operator: 48 operands: 47
44	ExprTuple	63
45	Operation	operator: 48 operands: 49
46	NamedExprs	element: 50 targets: 53
47	NamedExprs	element: 51 targets: 53
48	Literal
49	NamedExprs	element: 52 targets: 53
50	Operation	operator: 54 operands: 55
51	Operation	operator: 56 operands: 57
52	Operation	operator: 58 operands: 59
53	Operation	operator: 60 operands: 61
54	Literal
55	NamedExprs	state: 69 part: 63
56	Literal
57	NamedExprs	operation: 68 part: 63
58	Literal
59	NamedExprs	state: 62 part: 63
60	Literal
61	ExprTuple	64, 65
62	Operation	operator: 66 operands: 67
63	Variable
64	Literal
65	Variable
66	Literal
67	ExprTuple	68, 69
68	Variable
69	Variable