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 import l
from proveit.logic import Equals
from proveit.numbers import Add, Mod, ModAbs, subtract
from proveit.physics.quantum.QPE import _b_floor, _two_pow_t

# build up the expression from sub-expressions
expr = Equals(ModAbs(subtract(Mod(Add(_b_floor, l), _two_pow_t), _b_floor), _two_pow_t), ModAbs(l, _two_pow_t)).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} \left|\left(\left(b_{\textit{f}} + l\right) ~\textup{mod}~ 2^{t}\right) - b_{\textit{f}}\right|_{\textup{mod}\thinspace 2^{t}} =  \\ \left|l\right|_{\textup{mod}\thinspace 2^{t}} \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, 17
6	Literal
7	ExprTuple	23, 17
8	Operation	operator: 18 operands: 9
9	ExprTuple	10, 11
10	Operation	operator: 12 operands: 13
11	Operation	operator: 14 operand: 22
12	Literal
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	22
16	Operation	operator: 18 operands: 19
17	Operation	operator: 20 operands: 21
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24, 25
22	Literal
23	Variable
24	Literal
25	Literal