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, LessEq, Mult, 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(Abs(_rel_indexed_alpha), frac(one, Mult(two, Mult(_two_pow_t, Abs(subtract(_delta_b_floor, frac(l, _two_pow_t)))))))

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| \leq \frac{1}{2 \cdot \left(2^{t} \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: 20 operand: 7
4	Operation	operator: 33 operands: 6
5	ExprTuple	7
6	ExprTuple	8, 9
7	Operation	operator: 10 operand: 13
8	Literal
9	Operation	operator: 17 operands: 12
10	Literal
11	ExprTuple	13
12	ExprTuple	39, 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	31, 35
17	Literal
18	ExprTuple	36, 19
19	Operation	operator: 20 operand: 22
20	Literal
21	ExprTuple	22
22	Operation	operator: 23 operands: 24
23	Literal
24	ExprTuple	25, 26
25	Operation	operator: 27 operand: 31
26	Operation	operator: 29 operand: 32
27	Literal
28	ExprTuple	31
29	Literal
30	ExprTuple	32
31	Literal
32	Operation	operator: 33 operands: 34
33	Literal
34	ExprTuple	35, 36
35	Variable
36	Operation	operator: 37 operands: 38
37	Literal
38	ExprTuple	39, 40
39	Literal
40	Literal