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 m
from proveit.logic import And, InSet
from proveit.numbers import Exp, LessEq, ModAbs, one, subtract, two
from proveit.physics.quantum.QPE import _b_floor, _m_domain, _n, _t, _two_pow_t

# build up the expression from sub-expressions
expr = And(InSet(m, _m_domain), LessEq(ModAbs(subtract(m, _b_floor), _two_pow_t), subtract(Exp(two, subtract(_t, _n)), one)))

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(m \in \{0~\ldotp \ldotp~2^{t} - 1\}\right) \land \left(\left|m - b_{\textit{f}}\right|_{\textup{mod}\thinspace 2^{t}} \leq \left(2^{t - n} - 1\right)\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
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	26, 9
7	Literal
8	ExprTuple	10, 11
9	Operation	operator: 12 operands: 13
10	Operation	operator: 14 operands: 15
11	Operation	operator: 33 operands: 16
12	Literal
13	ExprTuple	17, 18
14	Literal
15	ExprTuple	19, 24
16	ExprTuple	20, 25
17	Literal
18	Operation	operator: 33 operands: 21
19	Operation	operator: 33 operands: 22
20	Operation	operator: 29 operands: 23
21	ExprTuple	24, 25
22	ExprTuple	26, 27
23	ExprTuple	35, 28
24	Operation	operator: 29 operands: 30
25	Operation	operator: 40 operand: 36
26	Variable
27	Operation	operator: 40 operand: 37
28	Operation	operator: 33 operands: 34
29	Literal
30	ExprTuple	35, 38
31	ExprTuple	36
32	ExprTuple	37
33	Literal
34	ExprTuple	38, 39
35	Literal
36	Literal
37	Literal
38	Literal
39	Operation	operator: 40 operand: 42
40	Literal
41	ExprTuple	42
42	Literal