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 Add, Exp, Mult, Neg, frac, one, pi, two
from proveit.physics.quantum.QPE import _delta_b_floor, _t

# build up the expression from sub-expressions
sub_expr1 = frac(one, two)
sub_expr2 = Exp(pi, Neg(one))
sub_expr3 = Add(Neg(Mult(l, Exp(two, Neg(_t)))), _delta_b_floor)
expr = Equals(Mult(two, pi, sub_expr3, Mult(sub_expr1, sub_expr2)), Mult(two, pi, sub_expr3, sub_expr1, sub_expr2)).with_wrapping_at(2)

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())

\begin{array}{c} \begin{array}{l} \left(2 \cdot \pi \cdot \left(-\left(l \cdot 2^{-t}\right) + \delta_{b_{\textit{f}}}\right) \cdot \left(\frac{1}{2} \cdot \pi^{-1}\right)\right) =  \\ \left(2 \cdot \pi \cdot \left(-\left(l \cdot 2^{-t}\right) + \delta_{b_{\textit{f}}}\right) \cdot \frac{1}{2} \cdot \pi^{-1}\right) \end{array} \end{array}

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.	()	(2)	('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: 27 operands: 5
4	Operation	operator: 27 operands: 6
5	ExprTuple	34, 22, 8, 7
6	ExprTuple	34, 22, 8, 12, 13
7	Operation	operator: 27 operands: 9
8	Operation	operator: 10 operands: 11
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	14, 15
12	Operation	operator: 16 operands: 17
13	Operation	operator: 32 operands: 18
14	Operation	operator: 36 operand: 24
15	Operation	operator: 20 operand: 25
16	Literal
17	ExprTuple	29, 34
18	ExprTuple	22, 23
19	ExprTuple	24
20	Literal
21	ExprTuple	25
22	Literal
23	Operation	operator: 36 operand: 29
24	Operation	operator: 27 operands: 28
25	Literal
26	ExprTuple	29
27	Literal
28	ExprTuple	30, 31
29	Literal
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