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, frac, one, subtract, two
from proveit.physics.quantum.QPE import _two_pow__t_minus_one

# build up the expression from sub-expressions
sub_expr1 = frac(one, Exp(e, two))
sub_expr2 = 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(Add(sub_expr2, sub_expr2, sub_expr1), Add(Mult(two, sub_expr2), sub_expr1)).with_wrapping_at(2)

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())

\begin{array}{c} \begin{array}{l} \left(\left(\sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{2}}\right) + \left(\sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{2}}\right) + \frac{1}{e^{2}}\right) =  \\ \left(\left(2 \cdot \left(\sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{2}}\right)\right) + \frac{1}{e^{2}}\right) \end{array} \end{array}

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.	()	(2)	('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: 42 operands: 5
4	Operation	operator: 42 operands: 6
5	ExprTuple	12, 12, 8
6	ExprTuple	7, 8
7	Operation	operator: 9 operands: 10
8	Operation	operator: 22 operands: 11
9	Literal
10	ExprTuple	40, 12
11	ExprTuple	48, 13
12	Operation	operator: 14 operand: 17
13	Operation	operator: 38 operands: 16
14	Literal
15	ExprTuple	17
16	ExprTuple	36, 40
17	Lambda	parameter: 31 body: 19
18	ExprTuple	31
19	Conditional	value: 20 condition: 21
20	Operation	operator: 22 operands: 23
21	Operation	operator: 24 operands: 25
22	Literal
23	ExprTuple	48, 26
24	Literal
25	ExprTuple	31, 27
26	Operation	operator: 38 operands: 28
27	Operation	operator: 29 operands: 30
28	ExprTuple	31, 40
29	Literal
30	ExprTuple	32, 33
31	Variable
32	Operation	operator: 42 operands: 34
33	Operation	operator: 42 operands: 35
34	ExprTuple	36, 48
35	ExprTuple	37, 45
36	Variable
37	Operation	operator: 38 operands: 39
38	Literal
39	ExprTuple	40, 41
40	Literal
41	Operation	operator: 42 operands: 43
42	Literal
43	ExprTuple	44, 45
44	Literal
45	Operation	operator: 46 operand: 48
46	Literal
47	ExprTuple	48
48	Literal