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 Abs, Exp, Mult, Neg, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _t, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = Abs(subtract(_delta_b_floor, Mult(l, Exp(two, Neg(_t)))))
expr = Equals(Mult(Mult(two, _two_pow_t), sub_expr1), Mult(two, _two_pow_t, sub_expr1)).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(2 \cdot 2^{t}\right) \cdot \left|\delta_{b_{\textit{f}}} - \left(l \cdot 2^{-t}\right)\right|\right) =  \\ \left(2 \cdot 2^{t} \cdot \left|\delta_{b_{\textit{f}}} - \left(l \cdot 2^{-t}\right)\right|\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: 24 operands: 5
4	Operation	operator: 24 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	30, 12, 8
7	Operation	operator: 24 operands: 9
8	Operation	operator: 10 operand: 13
9	ExprTuple	30, 12
10	Literal
11	ExprTuple	13
12	Operation	operator: 28 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	30, 34
15	Literal
16	ExprTuple	17, 18
17	Operation	operator: 19 operand: 22
18	Operation	operator: 32 operand: 23
19	Literal
20	ExprTuple	22
21	ExprTuple	23
22	Literal
23	Operation	operator: 24 operands: 25
24	Literal
25	ExprTuple	26, 27
26	Variable
27	Operation	operator: 28 operands: 29
28	Literal
29	ExprTuple	30, 31
30	Literal
31	Operation	operator: 32 operand: 34
32	Literal
33	ExprTuple	34
34	Literal