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, Neg, frac, one, pi, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _t

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