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 Equals, InSet
from proveit.numbers import Abs, ModAbs
from proveit.physics.quantum.QPE import _full_domain, _two_pow_t

# build up the expression from sub-expressions
expr = Conditional(Equals(ModAbs(l, _two_pow_t), Abs(l)), 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|l\right|_{\textup{mod}\thinspace 2^{t}} = \left|l\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: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	17, 9
7	Operation	operator: 10 operands: 11
8	Operation	operator: 12 operand: 17
9	Operation	operator: 14 operands: 15
10	Literal
11	ExprTuple	17, 16
12	Literal
13	ExprTuple	17
14	Literal
15	ExprTuple	18, 23
16	Operation	operator: 24 operands: 19
17	Variable
18	Operation	operator: 28 operands: 20
19	ExprTuple	26, 30
20	ExprTuple	21, 34
21	Operation	operator: 32 operand: 23
22	ExprTuple	23
23	Operation	operator: 24 operands: 25
24	Literal
25	ExprTuple	26, 27
26	Literal
27	Operation	operator: 28 operands: 29
28	Literal
29	ExprTuple	30, 31
30	Literal
31	Operation	operator: 32 operand: 34
32	Literal
33	ExprTuple	34
34	Literal