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, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _t, _two_pow_t

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