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, e, l
from proveit.core_expr_types import Len
from proveit.logic import Equals
from proveit.numbers import Add, Exp, Interval, Mult, Sum, frac, one, subtract, two
from proveit.physics.quantum.QPE import _two_pow__t_minus_one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Equals(Len(operands = [Mult(two, Sum(index_or_indices = [l], summand = frac(one, Exp(l, two)), domain = Interval(Add(e, one), subtract(_two_pow__t_minus_one, one)))), frac(one, Exp(e, two))]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, two)]))

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(2 \cdot \left(\sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{2}}\right), \frac{1}{e^{2}}\right)| = |\left(1, \ldots, 2\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	Operation	operator: 11 operands: 12
9	Operation	operator: 27 operands: 13
10	ExprRange	lambda_map: 14 start_index: 53 end_index: 45
11	Literal
12	ExprTuple	45, 15
13	ExprTuple	53, 16
14	Lambda	parameter: 21 body: 21
15	Operation	operator: 18 operand: 22
16	Operation	operator: 43 operands: 20
17	ExprTuple	21
18	Literal
19	ExprTuple	22
20	ExprTuple	41, 45
21	Variable
22	Lambda	parameter: 36 body: 24
23	ExprTuple	36
24	Conditional	value: 25 condition: 26
25	Operation	operator: 27 operands: 28
26	Operation	operator: 29 operands: 30
27	Literal
28	ExprTuple	53, 31
29	Literal
30	ExprTuple	36, 32
31	Operation	operator: 43 operands: 33
32	Operation	operator: 34 operands: 35
33	ExprTuple	36, 45
34	Literal
35	ExprTuple	37, 38
36	Variable
37	Operation	operator: 47 operands: 39
38	Operation	operator: 47 operands: 40
39	ExprTuple	41, 53
40	ExprTuple	42, 50
41	Variable
42	Operation	operator: 43 operands: 44
43	Literal
44	ExprTuple	45, 46
45	Literal
46	Operation	operator: 47 operands: 48
47	Literal
48	ExprTuple	49, 50
49	Literal
50	Operation	operator: 51 operand: 53
51	Literal
52	ExprTuple	53
53	Literal