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, k
from proveit.logic import InSet
from proveit.numbers import Exp, LessEq, Mult, frac, one, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _pos_domain, _two_pow_t

# build up the expression from sub-expressions
expr = Conditional(LessEq(frac(one, Exp(subtract(k, Mult(_two_pow_t, _delta_b_floor)), two)), frac(one, Exp(subtract(k, one), two))), InSet(k, _pos_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\{\frac{1}{\left(k - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}} \leq \frac{1}{\left(k - 1\right)^{2}} \textrm{ if } k \in \{e + 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: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	32, 9
7	Operation	operator: 11 operands: 10
8	Operation	operator: 11 operands: 12
9	Operation	operator: 13 operands: 14
10	ExprTuple	38, 15
11	Literal
12	ExprTuple	38, 16
13	Literal
14	ExprTuple	17, 18
15	Operation	operator: 43 operands: 19
16	Operation	operator: 43 operands: 20
17	Operation	operator: 29 operands: 21
18	Operation	operator: 43 operands: 22
19	ExprTuple	23, 47
20	ExprTuple	24, 47
21	ExprTuple	25, 38
22	ExprTuple	47, 26
23	Operation	operator: 29 operands: 27
24	Operation	operator: 29 operands: 28
25	Variable
26	Operation	operator: 29 operands: 30
27	ExprTuple	32, 31
28	ExprTuple	32, 33
29	Literal
30	ExprTuple	48, 33
31	Operation	operator: 35 operand: 37
32	Variable
33	Operation	operator: 35 operand: 38
34	ExprTuple	37
35	Literal
36	ExprTuple	38
37	Operation	operator: 39 operands: 40
38	Literal
39	Literal
40	ExprTuple	41, 42
41	Operation	operator: 43 operands: 44
42	Operation	operator: 45 operand: 49
43	Literal
44	ExprTuple	47, 48
45	Literal
46	ExprTuple	49
47	Literal
48	Literal
49	Literal