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 _pos_domain, _rel_indexed_alpha

# build up the expression from sub-expressions
expr = Conditional(InSet(Exp(Abs(_rel_indexed_alpha), two), Real), InSet(l, _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\{\left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2} \in \mathbb{R} \textrm{ if } l \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: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	36, 8
6	Operation	operator: 18 operands: 9
7	Literal
8	Operation	operator: 10 operands: 11
9	ExprTuple	12, 22
10	Literal
11	ExprTuple	13, 14
12	Operation	operator: 15 operand: 20
13	Operation	operator: 26 operands: 17
14	Operation	operator: 18 operands: 19
15	Literal
16	ExprTuple	20
17	ExprTuple	21, 37
18	Literal
19	ExprTuple	22, 23
20	Operation	operator: 24 operand: 28
21	Variable
22	Literal
23	Operation	operator: 26 operands: 27
24	Literal
25	ExprTuple	28
26	Literal
27	ExprTuple	29, 30
28	Operation	operator: 31 operands: 32
29	Literal
30	Operation	operator: 33 operand: 37
31	Literal
32	ExprTuple	35, 36
33	Literal
34	ExprTuple	37
35	Literal
36	Variable
37	Literal