Expression of type Equals

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.logic import Equals
from proveit.numbers import Abs, Add, Max, Neg, one, subtract
from proveit.physics.quantum.QPE import _two_pow__t_minus_one

# build up the expression from sub-expressions
expr = Equals(Max(Abs(Add(Neg(_two_pow__t_minus_one), one)), Abs(_two_pow__t_minus_one)), Max(subtract(_two_pow__t_minus_one, one), _two_pow__t_minus_one)).with_wrapping_at(2)

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())

\begin{array}{c} \begin{array}{l} {\rm Max}\left(\left|-2^{t - 1} + 1\right|, \left|2^{t - 1}\right|\right) =  \\ {\rm Max}\left(2^{t - 1} - 1, 2^{t - 1}\right) \end{array} \end{array}

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.	()	(2)	('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',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# 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: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 18
8	Operation	operator: 12 operand: 14
9	Operation	operator: 12 operand: 18
10	Operation	operator: 23 operands: 13
11	ExprTuple	14
12	Literal
13	ExprTuple	18, 26
14	Operation	operator: 23 operands: 15
15	ExprTuple	16, 29
16	Operation	operator: 27 operand: 18
17	ExprTuple	18
18	Operation	operator: 19 operands: 20
19	Literal
20	ExprTuple	21, 22
21	Literal
22	Operation	operator: 23 operands: 24
23	Literal
24	ExprTuple	25, 26
25	Literal
26	Operation	operator: 27 operand: 29
27	Literal
28	ExprTuple	29
29	Literal