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, l
from proveit.logic import And, Equals, InSet, TRUE
from proveit.numbers import Abs, Exp, two
from proveit.physics.quantum.QPE import _neg_domain, _rel_indexed_alpha

# build up the expression from sub-expressions
sub_expr1 = Exp(Abs(_rel_indexed_alpha), two)
sub_expr2 = InSet(l, _neg_domain)
expr = Equals(Conditional(sub_expr1, And(sub_expr2, TRUE)), Conditional(sub_expr1, sub_expr2)).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)\} ,  \top\right.. \\  = \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.. \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: 10
5	Operation	operator: 7 operands: 8
6	Operation	operator: 38 operands: 9
7	Literal
8	ExprTuple	10, 11
9	ExprTuple	12, 40
10	Operation	operator: 13 operands: 14
11	Literal
12	Operation	operator: 15 operand: 18
13	Literal
14	ExprTuple	33, 17
15	Literal
16	ExprTuple	18
17	Operation	operator: 19 operands: 20
18	Operation	operator: 21 operand: 25
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	25
23	Operation	operator: 42 operands: 26
24	Operation	operator: 46 operand: 31
25	Operation	operator: 28 operands: 29
26	ExprTuple	30, 48
27	ExprTuple	31
28	Literal
29	ExprTuple	32, 33
30	Operation	operator: 46 operand: 36
31	Operation	operator: 42 operands: 35
32	Literal
33	Variable
34	ExprTuple	36
35	ExprTuple	37, 48
36	Operation	operator: 38 operands: 39
37	Variable
38	Literal
39	ExprTuple	40, 41
40	Literal
41	Operation	operator: 42 operands: 43
42	Literal
43	ExprTuple	44, 45
44	Literal
45	Operation	operator: 46 operand: 48
46	Literal
47	ExprTuple	48
48	Literal