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

# build up the expression from sub-expressions
sub_expr1 = Sum(index_or_indices = [l], summand = frac(one, Exp(l, two)), domain = Interval(Add(e, one), subtract(_two_pow__t_minus_one, one)))
expr = Equals(Mult(frac(one, four), Mult(two, sub_expr1)), Mult(frac(one, two), sub_expr1))

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(\frac{1}{4} \cdot \left(2 \cdot \left(\sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{2}}\right)\right)\right) = \left(\frac{1}{2} \cdot \left(\sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{2}}\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: 11 operands: 5
4	Operation	operator: 11 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	9, 15
7	Operation	operator: 23 operands: 10
8	Operation	operator: 11 operands: 12
9	Operation	operator: 23 operands: 13
10	ExprTuple	49, 14
11	Literal
12	ExprTuple	41, 15
13	ExprTuple	49, 41
14	Literal
15	Operation	operator: 16 operand: 18
16	Literal
17	ExprTuple	18
18	Lambda	parameter: 32 body: 20
19	ExprTuple	32
20	Conditional	value: 21 condition: 22
21	Operation	operator: 23 operands: 24
22	Operation	operator: 25 operands: 26
23	Literal
24	ExprTuple	49, 27
25	Literal
26	ExprTuple	32, 28
27	Operation	operator: 39 operands: 29
28	Operation	operator: 30 operands: 31
29	ExprTuple	32, 41
30	Literal
31	ExprTuple	33, 34
32	Variable
33	Operation	operator: 43 operands: 35
34	Operation	operator: 43 operands: 36
35	ExprTuple	37, 49
36	ExprTuple	38, 46
37	Variable
38	Operation	operator: 39 operands: 40
39	Literal
40	ExprTuple	41, 42
41	Literal
42	Operation	operator: 43 operands: 44
43	Literal
44	ExprTuple	45, 46
45	Literal
46	Operation	operator: 47 operand: 49
47	Literal
48	ExprTuple	49
49	Literal