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 Conditional, e, l
from proveit.logic import Equals, InSet
from proveit.numbers import Abs, Add, Exp, Interval, Neg, one, subtract, two
from proveit.physics.quantum.QPE import _neg_domain, _rel_indexed_alpha, _two_pow__t_minus_one

# build up the expression from sub-expressions
sub_expr1 = Exp(Abs(_rel_indexed_alpha), two)
expr = Equals(Conditional(sub_expr1, InSet(l, _neg_domain)), Conditional(sub_expr1, InSet(l, Interval(Add(Neg(_two_pow__t_minus_one), one), subtract(Neg(e), one))))).with_wrapping_at(1)

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|\alpha_{b_{\textit{f}} \oplus l}\right|^{2} \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\}\right.. \\  = \left\{\left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2} \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-e - 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.	()	(1)	('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	Conditional	value: 6 condition: 5
4	Conditional	value: 6 condition: 7
5	Operation	operator: 10 operands: 8
6	Operation	operator: 42 operands: 9
7	Operation	operator: 10 operands: 11
8	ExprTuple	39, 12
9	ExprTuple	13, 44
10	Literal
11	ExprTuple	39, 14
12	Operation	operator: 18 operands: 15
13	Operation	operator: 16 operand: 21
14	Operation	operator: 18 operands: 19
15	ExprTuple	22, 20
16	Literal
17	ExprTuple	21
18	Literal
19	ExprTuple	22, 23
20	Operation	operator: 50 operand: 29
21	Operation	operator: 25 operand: 30
22	Operation	operator: 46 operands: 27
23	Operation	operator: 46 operands: 28
24	ExprTuple	29
25	Literal
26	ExprTuple	30
27	ExprTuple	31, 52
28	ExprTuple	32, 49
29	Operation	operator: 46 operands: 33
30	Operation	operator: 34 operands: 35
31	Operation	operator: 50 operand: 40
32	Operation	operator: 50 operand: 41
33	ExprTuple	41, 52
34	Literal
35	ExprTuple	38, 39
36	ExprTuple	40
37	ExprTuple	41
38	Literal
39	Variable
40	Operation	operator: 42 operands: 43
41	Variable
42	Literal
43	ExprTuple	44, 45
44	Literal
45	Operation	operator: 46 operands: 47
46	Literal
47	ExprTuple	48, 49
48	Literal
49	Operation	operator: 50 operand: 52
50	Literal
51	ExprTuple	52
52	Literal