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 Exp, Mult, Real, four, frac, one, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _neg_domain

# build up the expression from sub-expressions
expr = Conditional(InSet(frac(one, Mult(four, Exp(_diff_l_scaled_delta_floor, two))), Real), InSet(l, _neg_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}{4 \cdot \left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}} \in \mathbb{R} \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\}\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: 9 operands: 10
7	Literal
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	45, 13
11	Literal
12	ExprTuple	14, 15
13	Operation	operator: 39 operands: 16
14	Operation	operator: 35 operands: 17
15	Operation	operator: 41 operand: 22
16	ExprTuple	19, 20
17	ExprTuple	21, 45
18	ExprTuple	22
19	Literal
20	Operation	operator: 46 operands: 23
21	Operation	operator: 41 operand: 27
22	Operation	operator: 35 operands: 25
23	ExprTuple	26, 50
24	ExprTuple	27
25	ExprTuple	28, 45
26	Operation	operator: 35 operands: 29
27	Operation	operator: 46 operands: 30
28	Variable
29	ExprTuple	31, 32
30	ExprTuple	50, 33
31	Variable
32	Operation	operator: 41 operand: 37
33	Operation	operator: 35 operands: 36
34	ExprTuple	37
35	Literal
36	ExprTuple	51, 38
37	Operation	operator: 39 operands: 40
38	Operation	operator: 41 operand: 45
39	Literal
40	ExprTuple	43, 44
41	Literal
42	ExprTuple	45
43	Operation	operator: 46 operands: 47
44	Operation	operator: 48 operand: 52
45	Literal
46	Literal
47	ExprTuple	50, 51
48	Literal
49	ExprTuple	52
50	Literal
51	Literal
52	Literal