Expression of type And

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 b, l
from proveit.logic import And, InSet, NotEquals, Set
from proveit.numbers import zero
from proveit.physics.quantum.QPE import _b_floor, _b_round, _full_domain

# build up the expression from sub-expressions
expr = And(InSet(b, Set(_b_floor, _b_round)), InSet(l, _full_domain), 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(b \in \left\{b_{\textit{f}}, b_{\textit{r}}\right\}\right) \land \left(l \in \{-2^{t - 1} + 1~\ldotp \ldotp~2^{t - 1}\}\right) \land \left(l \neq 0\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4, 5
3	Operation	operator: 7 operands: 6
4	Operation	operator: 7 operands: 8
5	Operation	operator: 9 operands: 10
6	ExprTuple	11, 12
7	Literal
8	ExprTuple	14, 13
9	Literal
10	ExprTuple	14, 15
11	Variable
12	Operation	operator: 16 operands: 17
13	Operation	operator: 18 operands: 19
14	Variable
15	Literal
16	Literal
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	22, 26
20	Literal
21	Literal
22	Operation	operator: 31 operands: 23
23	ExprTuple	24, 37
24	Operation	operator: 35 operand: 26
25	ExprTuple	26
26	Operation	operator: 27 operands: 28
27	Literal
28	ExprTuple	29, 30
29	Literal
30	Operation	operator: 31 operands: 32
31	Literal
32	ExprTuple	33, 34
33	Literal
34	Operation	operator: 35 operand: 37
35	Literal
36	ExprTuple	37
37	Literal