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

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