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, Neg, frac, subtract
from proveit.physics.quantum.QPE import _b_floor, _delta_b_floor, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = frac(_b_floor, _two_pow_t)
sub_expr2 = frac(l, _two_pow_t)
sub_expr3 = Neg(sub_expr1)
expr = Equals(Add(sub_expr1, _delta_b_floor, subtract(sub_expr3, sub_expr2)), Add(sub_expr1, _delta_b_floor, sub_expr3, Neg(sub_expr2))).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(\frac{b_{\textit{f}}}{2^{t}} + \delta_{b_{\textit{f}}} + \left(-\frac{b_{\textit{f}}}{2^{t}} - \frac{l}{2^{t}}\right)\right) =  \\ \left(\frac{b_{\textit{f}}}{2^{t}} + \delta_{b_{\textit{f}}} - \frac{b_{\textit{f}}}{2^{t}} - \frac{l}{2^{t}}\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: 9 operands: 5
4	Operation	operator: 9 operands: 6
5	ExprTuple	18, 8, 7
6	ExprTuple	18, 8, 13, 14
7	Operation	operator: 9 operands: 10
8	Operation	operator: 11 operand: 23
9	Literal
10	ExprTuple	13, 14
11	Literal
12	ExprTuple	23
13	Operation	operator: 16 operand: 18
14	Operation	operator: 16 operand: 19
15	ExprTuple	18
16	Literal
17	ExprTuple	19
18	Operation	operator: 21 operands: 20
19	Operation	operator: 21 operands: 22
20	ExprTuple	23, 25
21	Literal
22	ExprTuple	24, 25
23	Literal
24	Variable
25	Operation	operator: 26 operands: 27
26	Literal
27	ExprTuple	28, 29
28	Literal
29	Literal