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, Add(sub_expr1, sub_expr2)), Add(Mult(two, sub_expr2), 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(\left(\sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{2}}\right) + \left(\frac{1}{e^{2}} + \left(\sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{2}}\right)\right)\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)

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: 44 operands: 5
4	Operation	operator: 44 operands: 6
5	ExprTuple	13, 7
6	ExprTuple	8, 12
7	Operation	operator: 44 operands: 9
8	Operation	operator: 10 operands: 11
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	42, 13
12	Operation	operator: 24 operands: 14
13	Operation	operator: 15 operand: 18
14	ExprTuple	50, 17
15	Literal
16	ExprTuple	18
17	Operation	operator: 40 operands: 19
18	Lambda	parameter: 33 body: 21
19	ExprTuple	38, 42
20	ExprTuple	33
21	Conditional	value: 22 condition: 23
22	Operation	operator: 24 operands: 25
23	Operation	operator: 26 operands: 27
24	Literal
25	ExprTuple	50, 28
26	Literal
27	ExprTuple	33, 29
28	Operation	operator: 40 operands: 30
29	Operation	operator: 31 operands: 32
30	ExprTuple	33, 42
31	Literal
32	ExprTuple	34, 35
33	Variable
34	Operation	operator: 44 operands: 36
35	Operation	operator: 44 operands: 37
36	ExprTuple	38, 50
37	ExprTuple	39, 47
38	Variable
39	Operation	operator: 40 operands: 41
40	Literal
41	ExprTuple	42, 43
42	Literal
43	Operation	operator: 44 operands: 45
44	Literal
45	ExprTuple	46, 47
46	Literal
47	Operation	operator: 48 operand: 50
48	Literal
49	ExprTuple	50
50	Literal