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, Lambda, 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(Lambda(l, Conditional(sub_expr1, InSet(l, _neg_domain))), Lambda(l, Conditional(sub_expr1, InSet(l, Interval(Add(Neg(_two_pow__t_minus_one), one), subtract(Neg(e), 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[l \mapsto \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..\right] =  \\ \left[l \mapsto \left\{\left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2} \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-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.	()	(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	Lambda	parameter: 42 body: 5
4	Lambda	parameter: 42 body: 7
5	Conditional	value: 9 condition: 8
6	ExprTuple	42
7	Conditional	value: 9 condition: 10
8	Operation	operator: 13 operands: 11
9	Operation	operator: 45 operands: 12
10	Operation	operator: 13 operands: 14
11	ExprTuple	42, 15
12	ExprTuple	16, 47
13	Literal
14	ExprTuple	42, 17
15	Operation	operator: 21 operands: 18
16	Operation	operator: 19 operand: 24
17	Operation	operator: 21 operands: 22
18	ExprTuple	25, 23
19	Literal
20	ExprTuple	24
21	Literal
22	ExprTuple	25, 26
23	Operation	operator: 53 operand: 32
24	Operation	operator: 28 operand: 33
25	Operation	operator: 49 operands: 30
26	Operation	operator: 49 operands: 31
27	ExprTuple	32
28	Literal
29	ExprTuple	33
30	ExprTuple	34, 55
31	ExprTuple	35, 52
32	Operation	operator: 49 operands: 36
33	Operation	operator: 37 operands: 38
34	Operation	operator: 53 operand: 43
35	Operation	operator: 53 operand: 44
36	ExprTuple	44, 55
37	Literal
38	ExprTuple	41, 42
39	ExprTuple	43
40	ExprTuple	44
41	Literal
42	Variable
43	Operation	operator: 45 operands: 46
44	Variable
45	Literal
46	ExprTuple	47, 48
47	Literal
48	Operation	operator: 49 operands: 50
49	Literal
50	ExprTuple	51, 52
51	Literal
52	Operation	operator: 53 operand: 55
53	Literal
54	ExprTuple	55
55	Literal