Expression of type Div

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.numbers import Abs, Mult, frac, 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 = Abs(_delta_b_round)
expr = frac(Mult(two, Sin(Mult(_two_pow_t, pi, sub_expr1))), Mult(two, Sin(Mult(pi, 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())

\frac{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)}}

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',)
division	'inline': uses '/'; 'fraction': numerator over the denominator (also see 'frac' function)	fraction	fraction	('with_inline_style', 'with_fraction_style')

# 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: 15 operands: 5
4	Operation	operator: 15 operands: 6
5	ExprTuple	24, 7
6	ExprTuple	24, 8
7	Operation	operator: 10 operand: 12
8	Operation	operator: 10 operand: 13
9	ExprTuple	12
10	Literal
11	ExprTuple	13
12	Operation	operator: 15 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	17, 18, 19
15	Literal
16	ExprTuple	18, 19
17	Operation	operator: 20 operands: 21
18	Literal
19	Operation	operator: 22 operand: 26
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	26
24	Literal
25	Literal
26	Operation	operator: 27 operand: 29
27	Literal
28	ExprTuple	29
29	Literal