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, b, l
from proveit.logic import And, InSet, NotEquals, Set
from proveit.numbers import Integer, frac, zero
from proveit.physics.quantum.QPE import _b_floor, _b_round, _delta_b, _two_pow_t

# build up the expression from sub-expressions
expr = Conditional(NotEquals(_delta_b, frac(l, _two_pow_t)), And(InSet(b, Set(_b_floor, _b_round)), InSet(l, Integer), NotEquals(l, zero)))

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\{\delta_{b} \neq \frac{l}{2^{t}} \textrm{ if } b \in \left\{b_{\textit{f}}, b_{\textit{r}}\right\} ,  l \in \mathbb{Z} ,  l \neq 0\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: 18 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 9, 10
6	Operation	operator: 11 operand: 21
7	Operation	operator: 13 operands: 14
8	Operation	operator: 16 operands: 15
9	Operation	operator: 16 operands: 17
10	Operation	operator: 18 operands: 19
11	Literal
12	ExprTuple	21
13	Literal
14	ExprTuple	24, 20
15	ExprTuple	21, 22
16	Literal
17	ExprTuple	24, 23
18	Literal
19	ExprTuple	24, 25
20	Operation	operator: 26 operands: 27
21	Variable
22	Operation	operator: 28 operands: 29
23	Literal
24	Variable
25	Literal
26	Literal
27	ExprTuple	30, 31
28	Literal
29	ExprTuple	32, 33
30	Literal
31	Literal
32	Literal
33	Literal