Expression of type ExprTuple

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 ExprTuple, m, n
from proveit.logic import 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 = ExprTuple(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\}, \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
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	33, 7
5	Literal
6	ExprTuple	8, 9
7	Operation	operator: 10 operands: 11
8	Operation	operator: 12 operands: 13
9	Operation	operator: 36 operands: 14
10	Literal
11	ExprTuple	15, 16
12	Literal
13	ExprTuple	17, 32
14	ExprTuple	38, 18
15	Literal
16	Operation	operator: 20 operands: 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 30 operand: 26
19	ExprTuple	34, 23
20	Literal
21	ExprTuple	24, 25
22	ExprTuple	26
23	Operation	operator: 30 operand: 32
24	Operation	operator: 28 operands: 29
25	Operation	operator: 30 operand: 35
26	Variable
27	ExprTuple	32
28	Literal
29	ExprTuple	33, 34
30	Literal
31	ExprTuple	35
32	Literal
33	Variable
34	Operation	operator: 36 operands: 37
35	Variable
36	Literal
37	ExprTuple	38, 39
38	Literal
39	Variable