Expression of type Conditional

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 Conditional, l
from proveit.logic import InSet
from proveit.numbers import IntervalCO, Neg, frac, one, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _full_domain, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = frac(one, two)
expr = Conditional(InSet(subtract(_delta_b_floor, frac(l, _two_pow_t)), IntervalCO(Neg(sub_expr1), sub_expr1)), InSet(l, _full_domain))

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\{\left(\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\right) \in \left[-\frac{1}{2},\frac{1}{2}\right) \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~2^{t - 1}\}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	31, 8
6	Operation	operator: 39 operands: 9
7	Operation	operator: 10 operands: 11
8	Operation	operator: 12 operands: 13
9	ExprTuple	14, 15
10	Literal
11	ExprTuple	16, 25
12	Literal
13	ExprTuple	17, 33
14	Operation	operator: 18 operand: 23
15	Operation	operator: 43 operand: 24
16	Operation	operator: 43 operand: 25
17	Operation	operator: 39 operands: 22
18	Literal
19	ExprTuple	23
20	ExprTuple	24
21	ExprTuple	25
22	ExprTuple	26, 45
23	Literal
24	Operation	operator: 28 operands: 27
25	Operation	operator: 28 operands: 29
26	Operation	operator: 43 operand: 33
27	ExprTuple	31, 32
28	Literal
29	ExprTuple	45, 37
30	ExprTuple	33
31	Variable
32	Operation	operator: 35 operands: 34
33	Operation	operator: 35 operands: 36
34	ExprTuple	37, 41
35	Literal
36	ExprTuple	37, 38
37	Literal
38	Operation	operator: 39 operands: 40
39	Literal
40	ExprTuple	41, 42
41	Literal
42	Operation	operator: 43 operand: 45
43	Literal
44	ExprTuple	45
45	Literal