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, Add, Exp, Mult, Neg, e, i, one, pi, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _two_pow_t

# build up the expression from sub-expressions
expr = Equals(Add(Abs(one), Abs(Neg(Exp(e, Mult(two, pi, i, subtract(Mult(_two_pow_t, _delta_b_floor), l)))))), Add(one, one)).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(\left|1\right| + \left|-\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\left(2^{t} \cdot \delta_{b_{\textit{f}}}\right) - l\right)}\right|\right) =  \\ \left(1 + 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: 23 operands: 5
4	Operation	operator: 23 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	12, 12
7	Operation	operator: 10 operand: 12
8	Operation	operator: 10 operand: 13
9	ExprTuple	12
10	Literal
11	ExprTuple	13
12	Literal
13	Operation	operator: 29 operand: 15
14	ExprTuple	15
15	Operation	operator: 34 operands: 16
16	ExprTuple	17, 18
17	Literal
18	Operation	operator: 27 operands: 19
19	ExprTuple	38, 20, 21, 22
20	Literal
21	Literal
22	Operation	operator: 23 operands: 24
23	Literal
24	ExprTuple	25, 26
25	Operation	operator: 27 operands: 28
26	Operation	operator: 29 operand: 33
27	Literal
28	ExprTuple	31, 32
29	Literal
30	ExprTuple	33
31	Operation	operator: 34 operands: 35
32	Operation	operator: 36 operand: 40
33	Variable
34	Literal
35	ExprTuple	38, 39
36	Literal
37	ExprTuple	40
38	Literal
39	Literal
40	Literal