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, l
from proveit.logic import InSet
from proveit.numbers import Abs, Exp, LessEq, Mult, four, frac, one, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _pos_domain, _rel_indexed_alpha

# build up the expression from sub-expressions
expr = Lambda(l, Conditional(LessEq(Exp(Abs(_rel_indexed_alpha), two), frac(one, Mult(four, Exp(_diff_l_scaled_delta_floor, two)))), InSet(l, _pos_domain)))

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\{\left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2} \leq \frac{1}{4 \cdot \left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}} \textrm{ if } l \in \{e + 1~\ldotp \ldotp~2^{t - 1}\}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 43 body: 2
1	ExprTuple	43
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	43, 11
9	Operation	operator: 53 operands: 12
10	Operation	operator: 13 operands: 14
11	Operation	operator: 15 operands: 16
12	ExprTuple	17, 57
13	Literal
14	ExprTuple	45, 18
15	Literal
16	ExprTuple	19, 20
17	Operation	operator: 21 operand: 26
18	Operation	operator: 49 operands: 23
19	Operation	operator: 40 operands: 24
20	Operation	operator: 53 operands: 25
21	Literal
22	ExprTuple	26
23	ExprTuple	27, 28
24	ExprTuple	29, 45
25	ExprTuple	57, 30
26	Operation	operator: 31 operand: 35
27	Literal
28	Operation	operator: 53 operands: 33
29	Variable
30	Operation	operator: 40 operands: 34
31	Literal
32	ExprTuple	35
33	ExprTuple	36, 57
34	ExprTuple	58, 37
35	Operation	operator: 38 operands: 39
36	Operation	operator: 40 operands: 41
37	Operation	operator: 46 operand: 45
38	Literal
39	ExprTuple	59, 43
40	Literal
41	ExprTuple	43, 44
42	ExprTuple	45
43	Variable
44	Operation	operator: 46 operand: 48
45	Literal
46	Literal
47	ExprTuple	48
48	Operation	operator: 49 operands: 50
49	Literal
50	ExprTuple	51, 52
51	Operation	operator: 53 operands: 54
52	Operation	operator: 55 operand: 59
53	Literal
54	ExprTuple	57, 58
55	Literal
56	ExprTuple	59
57	Literal
58	Literal
59	Literal