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, l
from proveit.numbers import Abs, Less, LessEq, Mult, frac, pi, subtract, two, zero
from proveit.physics.quantum.QPE import _delta_b_floor, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = Mult(pi, Abs(subtract(_delta_b_floor, frac(l, _two_pow_t))))
expr = ExprTuple(Less(zero, sub_expr1), LessEq(sub_expr1, frac(pi, two)))

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(0 < \left(\pi \cdot \left|\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\right|\right), \left(\pi \cdot \left|\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\right|\right) \leq \frac{\pi}{2}\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	7, 8
5	Literal
6	ExprTuple	8, 9
7	Literal
8	Operation	operator: 10 operands: 11
9	Operation	operator: 28 operands: 12
10	Literal
11	ExprTuple	14, 13
12	ExprTuple	14, 34
13	Operation	operator: 15 operand: 17
14	Literal
15	Literal
16	ExprTuple	17
17	Operation	operator: 18 operands: 19
18	Literal
19	ExprTuple	20, 21
20	Operation	operator: 22 operand: 26
21	Operation	operator: 24 operand: 27
22	Literal
23	ExprTuple	26
24	Literal
25	ExprTuple	27
26	Literal
27	Operation	operator: 28 operands: 29
28	Literal
29	ExprTuple	30, 31
30	Variable
31	Operation	operator: 32 operands: 33
32	Literal
33	ExprTuple	34, 35
34	Literal
35	Literal