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 Exp, Mult, Neg, one, pi, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _t

# build up the expression from sub-expressions
sub_expr1 = subtract(_delta_b_floor, Mult(l, Exp(two, Neg(_t))))
expr = Equals(Mult(Mult(two, pi, sub_expr1), Exp(Mult(two, pi), Neg(one))), sub_expr1)

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(\left(2 \cdot \pi \cdot \left(\delta_{b_{\textit{f}}} - \left(l \cdot 2^{-t}\right)\right)\right) \cdot \left(2 \cdot \pi\right)^{-1}\right) = \left(\delta_{b_{\textit{f}}} - \left(l \cdot 2^{-t}\right)\right)

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.	()	()	('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, 9
3	Operation	operator: 25 operands: 4
4	ExprTuple	5, 6
5	Operation	operator: 25 operands: 7
6	Operation	operator: 29 operands: 8
7	ExprTuple	31, 18, 9
8	ExprTuple	10, 11
9	Operation	operator: 12 operands: 13
10	Operation	operator: 25 operands: 14
11	Operation	operator: 33 operand: 19
12	Literal
13	ExprTuple	16, 17
14	ExprTuple	31, 18
15	ExprTuple	19
16	Operation	operator: 20 operand: 23
17	Operation	operator: 33 operand: 24
18	Literal
19	Literal
20	Literal
21	ExprTuple	23
22	ExprTuple	24
23	Literal
24	Operation	operator: 25 operands: 26
25	Literal
26	ExprTuple	27, 28
27	Variable
28	Operation	operator: 29 operands: 30
29	Literal
30	ExprTuple	31, 32
31	Literal
32	Operation	operator: 33 operand: 35
33	Literal
34	ExprTuple	35
35	Literal