Expression of type Lambda

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 = Lambda(l, 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())

l \mapsto \left(\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}\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 41 body: 2
1	ExprTuple	41
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Conditional	value: 8 condition: 7
6	Conditional	value: 8 condition: 9
7	Operation	operator: 12 operands: 10
8	Operation	operator: 44 operands: 11
9	Operation	operator: 12 operands: 13
10	ExprTuple	41, 14
11	ExprTuple	15, 46
12	Literal
13	ExprTuple	41, 16
14	Operation	operator: 20 operands: 17
15	Operation	operator: 18 operand: 23
16	Operation	operator: 20 operands: 21
17	ExprTuple	24, 22
18	Literal
19	ExprTuple	23
20	Literal
21	ExprTuple	24, 25
22	Operation	operator: 52 operand: 31
23	Operation	operator: 27 operand: 32
24	Operation	operator: 48 operands: 29
25	Operation	operator: 48 operands: 30
26	ExprTuple	31
27	Literal
28	ExprTuple	32
29	ExprTuple	33, 54
30	ExprTuple	34, 51
31	Operation	operator: 48 operands: 35
32	Operation	operator: 36 operands: 37
33	Operation	operator: 52 operand: 42
34	Operation	operator: 52 operand: 43
35	ExprTuple	43, 54
36	Literal
37	ExprTuple	40, 41
38	ExprTuple	42
39	ExprTuple	43
40	Literal
41	Variable
42	Operation	operator: 44 operands: 45
43	Variable
44	Literal
45	ExprTuple	46, 47
46	Literal
47	Operation	operator: 48 operands: 49
48	Literal
49	ExprTuple	50, 51
50	Literal
51	Operation	operator: 52 operand: 54
52	Literal
53	ExprTuple	54
54	Literal