Expression of type Less

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, Less, 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)
sub_expr2 = Mult(pi, sub_expr1)
expr = Less(frac(Mult(two, _two_pow_t, sub_expr1), sub_expr2), frac(Sin(Mult(_two_pow_t, pi, sub_expr1)), Sin(sub_expr2)))

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 2^{t} \cdot \left|\delta_{b_{\textit{r}}}\right|}{\pi \cdot \left|\delta_{b_{\textit{r}}}\right|} < \frac{\sin{\left(2^{t} \cdot \pi \cdot \left|\delta_{b_{\textit{r}}}\right|\right)}}{\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',)
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, 16
6	Literal
7	ExprTuple	9, 10
8	Operation	operator: 18 operands: 11
9	Operation	operator: 13 operand: 15
10	Operation	operator: 13 operand: 16
11	ExprTuple	27, 20, 22
12	ExprTuple	15
13	Literal
14	ExprTuple	16
15	Operation	operator: 18 operands: 17
16	Operation	operator: 18 operands: 19
17	ExprTuple	20, 21, 22
18	Literal
19	ExprTuple	21, 22
20	Operation	operator: 23 operands: 24
21	Literal
22	Operation	operator: 25 operand: 29
23	Literal
24	ExprTuple	27, 28
25	Literal
26	ExprTuple	29
27	Literal
28	Literal
29	Operation	operator: 30 operand: 32
30	Literal
31	ExprTuple	32
32	Literal