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, n
from proveit.logic import And, InSet
from proveit.numbers import Exp, Interval, LessEq, ModAbs, Neg, frac, one, subtract, two, zero
from proveit.physics.quantum.QPE import phase, two_pow_t

# build up the expression from sub-expressions
expr = And(InSet(m, Interval(zero, subtract(two_pow_t, one))), LessEq(ModAbs(subtract(frac(m, two_pow_t), phase), one), Exp(two, Neg(n))))

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|\frac{m}{2^{t}} - \varphi\right|_{\textup{mod}\thinspace 1} \leq 2^{-n}\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	35, 9
7	Literal
8	ExprTuple	10, 11
9	Operation	operator: 12 operands: 13
10	Operation	operator: 14 operands: 15
11	Operation	operator: 38 operands: 16
12	Literal
13	ExprTuple	17, 18
14	Literal
15	ExprTuple	19, 34
16	ExprTuple	40, 20
17	Literal
18	Operation	operator: 22 operands: 21
19	Operation	operator: 22 operands: 23
20	Operation	operator: 32 operand: 28
21	ExprTuple	36, 25
22	Literal
23	ExprTuple	26, 27
24	ExprTuple	28
25	Operation	operator: 32 operand: 34
26	Operation	operator: 30 operands: 31
27	Operation	operator: 32 operand: 37
28	Variable
29	ExprTuple	34
30	Literal
31	ExprTuple	35, 36
32	Literal
33	ExprTuple	37
34	Literal
35	Variable
36	Operation	operator: 38 operands: 39
37	Variable
38	Literal
39	ExprTuple	40, 41
40	Literal
41	Variable