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 = Mult(two, _two_pow_t, Sin(Mult(pi, 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))))), sub_expr1), frac(two, 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{2}{2 \cdot 2^{t} \cdot \sin{\left(\pi \cdot \left|\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\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: 45 operands: 5
4	Operation	operator: 45 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	55, 8
7	Operation	operator: 24 operand: 11
8	Operation	operator: 41 operands: 10
9	ExprTuple	11
10	ExprTuple	55, 49, 12
11	Operation	operator: 35 operands: 13
12	Operation	operator: 14 operand: 18
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	18
16	Literal
17	Operation	operator: 43 operand: 21
18	Operation	operator: 41 operands: 20
19	ExprTuple	21
20	ExprTuple	31, 22
21	Operation	operator: 52 operands: 23
22	Operation	operator: 24 operand: 28
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	28
26	Literal
27	Operation	operator: 41 operands: 29
28	Operation	operator: 35 operands: 30
29	ExprTuple	55, 31, 32, 33
30	ExprTuple	47, 34
31	Literal
32	Literal
33	Operation	operator: 35 operands: 36
34	Operation	operator: 43 operand: 40
35	Literal
36	ExprTuple	38, 39
37	ExprTuple	40
38	Operation	operator: 41 operands: 42
39	Operation	operator: 43 operand: 48
40	Operation	operator: 45 operands: 46
41	Literal
42	ExprTuple	49, 47
43	Literal
44	ExprTuple	48
45	Literal
46	ExprTuple	48, 49
47	Operation	operator: 50 operand: 54
48	Variable
49	Operation	operator: 52 operands: 53
50	Literal
51	ExprTuple	54
52	Literal
53	ExprTuple	55, 56
54	Literal
55	Literal
56	Literal