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 Abs, Exp, Real, two
from proveit.physics.quantum.QPE import _neg_domain, _rel_indexed_alpha

# build up the expression from sub-expressions
expr = Conditional(InSet(Exp(Abs(_rel_indexed_alpha), 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\{\left|\alpha_{b_{\textit{f}} \oplus l}\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	34, 8
6	Operation	operator: 31 operands: 9
7	Literal
8	Operation	operator: 10 operands: 11
9	ExprTuple	12, 35
10	Literal
11	ExprTuple	13, 14
12	Operation	operator: 15 operand: 19
13	Operation	operator: 37 operands: 17
14	Operation	operator: 41 operand: 21
15	Literal
16	ExprTuple	19
17	ExprTuple	20, 43
18	ExprTuple	21
19	Operation	operator: 22 operand: 26
20	Operation	operator: 41 operand: 27
21	Operation	operator: 37 operands: 25
22	Literal
23	ExprTuple	26
24	ExprTuple	27
25	ExprTuple	28, 43
26	Operation	operator: 29 operands: 30
27	Operation	operator: 31 operands: 32
28	Variable
29	Literal
30	ExprTuple	33, 34
31	Literal
32	ExprTuple	35, 36
33	Literal
34	Variable
35	Literal
36	Operation	operator: 37 operands: 38
37	Literal
38	ExprTuple	39, 40
39	Literal
40	Operation	operator: 41 operand: 43
41	Literal
42	ExprTuple	43
43	Literal