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, four, frac, one, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _rel_indexed_alpha, _two_pow_t

# build up the expression from sub-expressions
expr = LessEq(Exp(Abs(_rel_indexed_alpha), two), frac(one, Mult(four, Exp(subtract(Mult(_two_pow_t, _delta_b_floor), l), 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|\alpha_{b_{\textit{f}} \oplus l}\right|^{2} \leq \frac{1}{4 \cdot \left(\left(2^{t} \cdot \delta_{b_{\textit{f}}}\right) - l\right)^{2}}

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: 35 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 39
6	Literal
7	ExprTuple	9, 10
8	Operation	operator: 11 operand: 14
9	Literal
10	Operation	operator: 28 operands: 13
11	Literal
12	ExprTuple	14
13	ExprTuple	15, 16
14	Operation	operator: 17 operand: 20
15	Literal
16	Operation	operator: 35 operands: 19
17	Literal
18	ExprTuple	20
19	ExprTuple	21, 39
20	Operation	operator: 22 operands: 23
21	Operation	operator: 24 operands: 25
22	Literal
23	ExprTuple	41, 34
24	Literal
25	ExprTuple	26, 27
26	Operation	operator: 28 operands: 29
27	Operation	operator: 30 operand: 34
28	Literal
29	ExprTuple	32, 33
30	Literal
31	ExprTuple	34
32	Operation	operator: 35 operands: 36
33	Operation	operator: 37 operand: 41
34	Variable
35	Literal
36	ExprTuple	39, 40
37	Literal
38	ExprTuple	41
39	Literal
40	Literal
41	Literal