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 = Mult(two, sub_expr1)
sub_expr3 = Mult(pi, sub_expr1)
expr = Equals(Mult(frac(one, _two_pow_t), frac(Mult(_two_pow_t, sub_expr2), sub_expr3)), Mult(frac(one, one), frac(sub_expr2, sub_expr3)))

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}{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}{1} \cdot \frac{2 \cdot \left|\delta_{b_{\textit{r}}}\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: 26 operands: 5
4	Operation	operator: 26 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	9, 10
7	Operation	operator: 14 operands: 11
8	Operation	operator: 14 operands: 12
9	Operation	operator: 14 operands: 13
10	Operation	operator: 14 operands: 15
11	ExprTuple	17, 21
12	ExprTuple	16, 18
13	ExprTuple	17, 17
14	Literal
15	ExprTuple	22, 18
16	Operation	operator: 26 operands: 19
17	Literal
18	Operation	operator: 26 operands: 20
19	ExprTuple	21, 22
20	ExprTuple	23, 30
21	Operation	operator: 24 operands: 25
22	Operation	operator: 26 operands: 27
23	Literal
24	Literal
25	ExprTuple	29, 28
26	Literal
27	ExprTuple	29, 30
28	Literal
29	Literal
30	Operation	operator: 31 operand: 33
31	Literal
32	ExprTuple	33
33	Operation	operator: 34 operand: 36
34	Literal
35	ExprTuple	36
36	Literal