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
from proveit.core_expr_types import Len
from proveit.logic import Equals
from proveit.numbers import Abs, Mult, one, pi, two
from proveit.physics.quantum.QPE import _delta_b_round, _two_pow_t
from proveit.trigonometry import Sin

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Abs(_delta_b_round)
expr = Equals(Len(operands = [Mult(two, Sin(Mult(_two_pow_t, pi, sub_expr2))), Mult(two, Sin(Mult(pi, 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(2 \cdot \sin{\left(2^{t} \cdot \pi \cdot \left|\delta_{b_{\textit{r}}}\right|\right)}, 2 \cdot \sin{\left(\pi \cdot \left|\delta_{b_{\textit{r}}}\right|\right)}\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: 25 operands: 11
9	Operation	operator: 25 operands: 12
10	ExprRange	lambda_map: 13 start_index: 14 end_index: 34
11	ExprTuple	34, 15
12	ExprTuple	34, 16
13	Lambda	parameter: 21 body: 21
14	Literal
15	Operation	operator: 19 operand: 22
16	Operation	operator: 19 operand: 23
17	ExprTuple	21
18	ExprTuple	22
19	Literal
20	ExprTuple	23
21	Variable
22	Operation	operator: 25 operands: 24
23	Operation	operator: 25 operands: 26
24	ExprTuple	27, 28, 29
25	Literal
26	ExprTuple	28, 29
27	Operation	operator: 30 operands: 31
28	Literal
29	Operation	operator: 32 operand: 36
30	Literal
31	ExprTuple	34, 35
32	Literal
33	ExprTuple	36
34	Literal
35	Literal
36	Operation	operator: 37 operand: 39
37	Literal
38	ExprTuple	39
39	Literal