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, Mult, frac, pi, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _two_pow_t
from proveit.trigonometry import Sin

# build up the expression from sub-expressions
sub_expr1 = Sin(Mult(pi, Abs(subtract(_delta_b_floor, frac(l, _two_pow_t)))))
expr = Equals(Mult(_two_pow_t, Mult(two, sub_expr1)), Mult(two, _two_pow_t, 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(2^{t} \cdot \left(2 \cdot \sin{\left(\pi \cdot \left|\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\right|\right)}\right)\right) = \left(2 \cdot 2^{t} \cdot \sin{\left(\pi \cdot \left|\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\right|\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, 4
3	Operation	operator: 13 operands: 5
4	Operation	operator: 13 operands: 6
5	ExprTuple	33, 7
6	ExprTuple	36, 33, 9
7	Operation	operator: 13 operands: 8
8	ExprTuple	36, 9
9	Operation	operator: 10 operand: 12
10	Literal
11	ExprTuple	12
12	Operation	operator: 13 operands: 14
13	Literal
14	ExprTuple	15, 16
15	Literal
16	Operation	operator: 17 operand: 19
17	Literal
18	ExprTuple	19
19	Operation	operator: 20 operands: 21
20	Literal
21	ExprTuple	22, 23
22	Operation	operator: 24 operand: 28
23	Operation	operator: 26 operand: 29
24	Literal
25	ExprTuple	28
26	Literal
27	ExprTuple	29
28	Literal
29	Operation	operator: 30 operands: 31
30	Literal
31	ExprTuple	32, 33
32	Variable
33	Operation	operator: 34 operands: 35
34	Literal
35	ExprTuple	36, 37
36	Literal
37	Literal