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, 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}")
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(Len(operands = [sub_expr2, sub_expr2]), 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(\sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{2}}, \sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{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, 8
6	Literal
7	ExprTuple	9
8	Operation	operator: 10 operand: 13
9	ExprRange	lambda_map: 12 start_index: 46 end_index: 38
10	Literal
11	ExprTuple	13
12	Lambda	parameter: 17 body: 17
13	Lambda	parameter: 29 body: 16
14	ExprTuple	17
15	ExprTuple	29
16	Conditional	value: 18 condition: 19
17	Variable
18	Operation	operator: 20 operands: 21
19	Operation	operator: 22 operands: 23
20	Literal
21	ExprTuple	46, 24
22	Literal
23	ExprTuple	29, 25
24	Operation	operator: 36 operands: 26
25	Operation	operator: 27 operands: 28
26	ExprTuple	29, 38
27	Literal
28	ExprTuple	30, 31
29	Variable
30	Operation	operator: 40 operands: 32
31	Operation	operator: 40 operands: 33
32	ExprTuple	34, 46
33	ExprTuple	35, 43
34	Variable
35	Operation	operator: 36 operands: 37
36	Literal
37	ExprTuple	38, 39
38	Literal
39	Operation	operator: 40 operands: 41
40	Literal
41	ExprTuple	42, 43
42	Literal
43	Operation	operator: 44 operand: 46
44	Literal
45	ExprTuple	46
46	Literal