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, Neg, frac, pi, subtract, two, zero
from proveit.physics.quantum.QPE import _delta_b_floor, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = Mult(two, pi, subtract(_delta_b_floor, frac(l, _two_pow_t)))
expr = Equals(Abs(subtract(zero, sub_expr1)), Abs(Neg(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|0 - \left(2 \cdot \pi \cdot \left(\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\right)\right)\right| = \left|-\left(2 \cdot \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: 6 operand: 8
4	Operation	operator: 6 operand: 11
5	ExprTuple	8
6	Literal
7	ExprTuple	11
8	Operation	operator: 18 operands: 9
9	ExprTuple	10, 11
10	Literal
11	Operation	operator: 24 operand: 13
12	ExprTuple	13
13	Operation	operator: 14 operands: 15
14	Literal
15	ExprTuple	34, 16, 17
16	Literal
17	Operation	operator: 18 operands: 19
18	Literal
19	ExprTuple	20, 21
20	Operation	operator: 22 operand: 26
21	Operation	operator: 24 operand: 27
22	Literal
23	ExprTuple	26
24	Literal
25	ExprTuple	27
26	Literal
27	Operation	operator: 28 operands: 29
28	Literal
29	ExprTuple	30, 31
30	Variable
31	Operation	operator: 32 operands: 33
32	Literal
33	ExprTuple	34, 35
34	Literal
35	Literal