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.logic import Equals
from proveit.numbers import Abs, Mult, frac, one, pi, two
from proveit.physics.quantum.QPE import _delta_b_round, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = Abs(_delta_b_round)
sub_expr2 = frac(Mult(_two_pow_t, Mult(two, sub_expr1)), Mult(pi, sub_expr1))
expr = Equals(Mult(frac(one, Mult(one, _two_pow_t)), sub_expr2), Mult(frac(one, _two_pow_t), sub_expr2))

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(\frac{1}{1 \cdot 2^{t}} \cdot \frac{2^{t} \cdot \left(2 \cdot \left|\delta_{b_{\textit{r}}}\right|\right)}{\pi \cdot \left|\delta_{b_{\textit{r}}}\right|}\right) = \left(\frac{1}{2^{t}} \cdot \frac{2^{t} \cdot \left(2 \cdot \left|\delta_{b_{\textit{r}}}\right|\right)}{\pi \cdot \left|\delta_{b_{\textit{r}}}\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: 25 operands: 5
4	Operation	operator: 25 operands: 6
5	ExprTuple	7, 9
6	ExprTuple	8, 9
7	Operation	operator: 11 operands: 10
8	Operation	operator: 11 operands: 16
9	Operation	operator: 11 operands: 12
10	ExprTuple	19, 13
11	Literal
12	ExprTuple	14, 15
13	Operation	operator: 25 operands: 16
14	Operation	operator: 25 operands: 17
15	Operation	operator: 25 operands: 18
16	ExprTuple	19, 20
17	ExprTuple	20, 21
18	ExprTuple	22, 29
19	Literal
20	Operation	operator: 23 operands: 24
21	Operation	operator: 25 operands: 26
22	Literal
23	Literal
24	ExprTuple	28, 27
25	Literal
26	ExprTuple	28, 29
27	Literal
28	Literal
29	Operation	operator: 30 operand: 32
30	Literal
31	ExprTuple	32
32	Operation	operator: 33 operand: 35
33	Literal
34	ExprTuple	35
35	Literal