Expression of type And

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.logic import And
from proveit.numbers import Abs, LessEq, Mult, frac, one, subtract, two, zero
from proveit.physics.quantum.QPE import _delta_b_floor, _rel_indexed_alpha, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = Abs(_rel_indexed_alpha)
expr = And(LessEq(zero, sub_expr1), LessEq(sub_expr1, frac(one, Mult(two, Abs(subtract(Mult(_two_pow_t, _delta_b_floor), l))))))

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(0 \leq \left|\alpha_{b_{\textit{f}} \oplus l}\right|\right) \land \left(\left|\alpha_{b_{\textit{f}} \oplus l}\right| \leq \frac{1}{2 \cdot \left|\left(2^{t} \cdot \delta_{b_{\textit{f}}}\right) - l\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',)
as_total_ordering	When 'True', style the conjunction as a total ordering (e.g. x < y < z from (x < y) and (y < z))	None	None/False	('with_total_ordering_style',)

# 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, 9
6	Literal
7	ExprTuple	9, 10
8	Literal
9	Operation	operator: 24 operand: 14
10	Operation	operator: 12 operands: 13
11	ExprTuple	14
12	Literal
13	ExprTuple	15, 16
14	Operation	operator: 17 operand: 20
15	Literal
16	Operation	operator: 31 operands: 19
17	Literal
18	ExprTuple	20
19	ExprTuple	42, 21
20	Operation	operator: 22 operands: 23
21	Operation	operator: 24 operand: 26
22	Literal
23	ExprTuple	44, 37
24	Literal
25	ExprTuple	26
26	Operation	operator: 27 operands: 28
27	Literal
28	ExprTuple	29, 30
29	Operation	operator: 31 operands: 32
30	Operation	operator: 33 operand: 37
31	Literal
32	ExprTuple	35, 36
33	Literal
34	ExprTuple	37
35	Operation	operator: 38 operands: 39
36	Operation	operator: 40 operand: 44
37	Variable
38	Literal
39	ExprTuple	42, 43
40	Literal
41	ExprTuple	44
42	Literal
43	Literal
44	Literal