Expression of type LessEq

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 l
from proveit.numbers import Abs, Exp, LessEq, Mult, e, frac, i, one, pi, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _two_pow_t
from proveit.trigonometry import Sin

# build up the expression from sub-expressions
sub_expr1 = Abs(subtract(_delta_b_floor, frac(l, _two_pow_t)))
expr = LessEq(frac(Abs(subtract(one, Exp(e, Mult(two, pi, i, subtract(Mult(_two_pow_t, _delta_b_floor), l))))), Mult(two, _two_pow_t, Sin(Mult(pi, sub_expr1)))), frac(one, Mult(two, _two_pow_t, 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{\left|1 - \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\left(2^{t} \cdot \delta_{b_{\textit{f}}}\right) - l\right)}\right|}{2 \cdot 2^{t} \cdot \sin{\left(\pi \cdot \left|\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\right|\right)}} \leq \frac{1}{2 \cdot 2^{t} \cdot \left|\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\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: 47 operands: 5
4	Operation	operator: 47 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	18, 9
7	Operation	operator: 26 operand: 13
8	Operation	operator: 43 operands: 11
9	Operation	operator: 43 operands: 12
10	ExprTuple	13
11	ExprTuple	57, 51, 14
12	ExprTuple	57, 51, 24
13	Operation	operator: 37 operands: 15
14	Operation	operator: 16 operand: 20
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20
18	Literal
19	Operation	operator: 45 operand: 23
20	Operation	operator: 43 operands: 22
21	ExprTuple	23
22	ExprTuple	33, 24
23	Operation	operator: 54 operands: 25
24	Operation	operator: 26 operand: 30
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	30
28	Literal
29	Operation	operator: 43 operands: 31
30	Operation	operator: 37 operands: 32
31	ExprTuple	57, 33, 34, 35
32	ExprTuple	49, 36
33	Literal
34	Literal
35	Operation	operator: 37 operands: 38
36	Operation	operator: 45 operand: 42
37	Literal
38	ExprTuple	40, 41
39	ExprTuple	42
40	Operation	operator: 43 operands: 44
41	Operation	operator: 45 operand: 50
42	Operation	operator: 47 operands: 48
43	Literal
44	ExprTuple	51, 49
45	Literal
46	ExprTuple	50
47	Literal
48	ExprTuple	50, 51
49	Operation	operator: 52 operand: 56
50	Variable
51	Operation	operator: 54 operands: 55
52	Literal
53	ExprTuple	56
54	Literal
55	ExprTuple	57, 58
56	Literal
57	Literal
58	Literal