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, four, 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 = Neg(one)
sub_expr2 = Exp(two, Neg(_t))
sub_expr3 = Abs(subtract(_delta_b_floor, Mult(l, sub_expr2)))
expr = Equals(Mult(two, Exp(Mult(four, _two_pow_t, sub_expr3), sub_expr1)), Mult(two, Mult(frac(one, four), sub_expr2, Exp(sub_expr3, 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 \cdot \left(4 \cdot 2^{t} \cdot \left|\delta_{b_{\textit{f}}} - \left(l \cdot 2^{-t}\right)\right|\right)^{-1}\right) = \left(2 \cdot \left(\frac{1}{4} \cdot 2^{-t} \cdot \left|\delta_{b_{\textit{f}}} - \left(l \cdot 2^{-t}\right)\right|^{-1}\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: 37 operands: 5
4	Operation	operator: 37 operands: 6
5	ExprTuple	43, 7
6	ExprTuple	43, 8
7	Operation	operator: 41 operands: 9
8	Operation	operator: 37 operands: 10
9	ExprTuple	11, 21
10	ExprTuple	12, 40, 13
11	Operation	operator: 37 operands: 14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 41 operands: 17
14	ExprTuple	19, 18, 20
15	Literal
16	ExprTuple	27, 19
17	ExprTuple	20, 21
18	Operation	operator: 41 operands: 22
19	Literal
20	Operation	operator: 23 operand: 26
21	Operation	operator: 45 operand: 27
22	ExprTuple	43, 47
23	Literal
24	ExprTuple	26
25	ExprTuple	27
26	Operation	operator: 28 operands: 29
27	Literal
28	Literal
29	ExprTuple	30, 31
30	Operation	operator: 32 operand: 35
31	Operation	operator: 45 operand: 36
32	Literal
33	ExprTuple	35
34	ExprTuple	36
35	Literal
36	Operation	operator: 37 operands: 38
37	Literal
38	ExprTuple	39, 40
39	Variable
40	Operation	operator: 41 operands: 42
41	Literal
42	ExprTuple	43, 44
43	Literal
44	Operation	operator: 45 operand: 47
45	Literal
46	ExprTuple	47
47	Literal