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

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

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} \cdot 2^{-t} \cdot \left|\delta_{b_{\textit{f}}} - \left(l \cdot 2^{-t}\right)\right|^{-1}\right) = \frac{1}{2 \cdot 2^{t} \cdot \left|\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\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: 36 operands: 5
4	Operation	operator: 38 operands: 6
5	ExprTuple	7, 40, 8
6	ExprTuple	21, 9
7	Operation	operator: 38 operands: 10
8	Operation	operator: 44 operands: 11
9	Operation	operator: 36 operands: 12
10	ExprTuple	21, 47
11	ExprTuple	13, 14
12	ExprTuple	47, 42, 15
13	Operation	operator: 18 operand: 20
14	Operation	operator: 48 operand: 21
15	Operation	operator: 18 operand: 22
16	ExprTuple	20
17	ExprTuple	21
18	Literal
19	ExprTuple	22
20	Operation	operator: 24 operands: 23
21	Literal
22	Operation	operator: 24 operands: 25
23	ExprTuple	27, 26
24	Literal
25	ExprTuple	27, 28
26	Operation	operator: 48 operand: 33
27	Operation	operator: 30 operand: 34
28	Operation	operator: 48 operand: 35
29	ExprTuple	33
30	Literal
31	ExprTuple	34
32	ExprTuple	35
33	Operation	operator: 36 operands: 37
34	Literal
35	Operation	operator: 38 operands: 39
36	Literal
37	ExprTuple	41, 40
38	Literal
39	ExprTuple	41, 42
40	Operation	operator: 44 operands: 43
41	Variable
42	Operation	operator: 44 operands: 45
43	ExprTuple	47, 46
44	Literal
45	ExprTuple	47, 50
46	Operation	operator: 48 operand: 50
47	Literal
48	Literal
49	ExprTuple	50
50	Literal