Expression of type Equals

from the theory of proveit.physics.quantum.QPE

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 ExprRange, Variable
from proveit.core_expr_types import Len
from proveit.logic import Equals
from proveit.numbers import Add, one
from proveit.physics.quantum import Z
from proveit.physics.quantum.QPE import _s, _s_wire, _t
from proveit.physics.quantum.circuits import Measure

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Equals(Len(operands = [ExprRange(sub_expr1, Measure(basis = Z), one, _t), _s_wire]), Len(operands = [ExprRange(sub_expr1, [Variable("_b", latex_format = r"{_{-}b}"), sub_expr1], one, Add(_t, _s))]))

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(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \meter 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \meter 
} \end{array}, ..\left(t - 3\right) \times.., \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \meter 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}, ..\left(s - 3\right) \times.., \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}\right)| = |\left(\left({_{-}b}, 1\right), \left({_{-}b}, 2\right), \ldots, \left({_{-}b}, t + s\right)\right)|

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10
8	ExprRange	lambda_map: 11 start_index: 14 end_index: 28
9	ExprRange	lambda_map: 12 start_index: 14 end_index: 29
10	ExprRange	lambda_map: 13 start_index: 14 end_index: 15
11	Lambda	parameter: 27 body: 16
12	Lambda	parameter: 27 body: 17
13	Lambda	parameter: 27 body: 19
14	Literal
15	Operation	operator: 20 operands: 21
16	Operation	operator: 22 operands: 23
17	Operation	operator: 24 operands: 25
18	ExprTuple	27
19	ExprTuple	26, 27
20	Literal
21	ExprTuple	28, 29
22	Literal
23	NamedExprs	basis: 30
24	Literal
25	NamedExprs	operation: 31
26	Variable
27	Variable
28	Literal
29	Literal
30	Literal
31	Literal