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

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

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())

\frac{1}{4 \cdot \left(\left(2^{t} \cdot \delta_{b_{\textit{f}}}\right) - l\right)^{2}} = \frac{1}{4 \cdot \left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}

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 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	9, 8
6	Literal
7	ExprTuple	9, 10
8	Operation	operator: 30 operands: 11
9	Literal
10	Operation	operator: 30 operands: 12
11	ExprTuple	14, 13
12	ExprTuple	14, 15
13	Operation	operator: 34 operands: 16
14	Literal
15	Operation	operator: 34 operands: 17
16	ExprTuple	18, 38
17	ExprTuple	19, 38
18	Operation	operator: 21 operands: 20
19	Operation	operator: 21 operands: 22
20	ExprTuple	29, 23
21	Literal
22	ExprTuple	28, 24
23	Operation	operator: 26 operand: 28
24	Operation	operator: 26 operand: 29
25	ExprTuple	28
26	Literal
27	ExprTuple	29
28	Variable
29	Operation	operator: 30 operands: 31
30	Literal
31	ExprTuple	32, 33
32	Operation	operator: 34 operands: 35
33	Operation	operator: 36 operand: 40
34	Literal
35	ExprTuple	38, 39
36	Literal
37	ExprTuple	40
38	Literal
39	Literal
40	Literal