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(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(\frac{1}{2} \cdot 2 \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: 26 operands: 5
4	Operation	operator: 26 operands: 6
5	ExprTuple	7, 32, 17, 8, 9
6	ExprTuple	25, 17, 8, 9
7	Operation	operator: 10 operands: 11
8	Operation	operator: 12 operands: 13
9	Operation	operator: 30 operands: 14
10	Literal
11	ExprTuple	25, 32
12	Literal
13	ExprTuple	15, 16
14	ExprTuple	17, 18
15	Operation	operator: 19 operand: 23
16	Operation	operator: 34 operand: 24
17	Literal
18	Operation	operator: 34 operand: 25
19	Literal
20	ExprTuple	23
21	ExprTuple	24
22	ExprTuple	25
23	Literal
24	Operation	operator: 26 operands: 27
25	Literal
26	Literal
27	ExprTuple	28, 29
28	Variable
29	Operation	operator: 30 operands: 31
30	Literal
31	ExprTuple	32, 33
32	Literal
33	Operation	operator: 34 operand: 36
34	Literal
35	ExprTuple	36
36	Literal