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 Exp, frac, one, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _pos_domain

# build up the expression from sub-expressions
expr = Lambda(l, Conditional(frac(one, 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\{\frac{1}{\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: 20 body: 2
1	ExprTuple	20
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	35, 9
7	Literal
8	ExprTuple	20, 10
9	Operation	operator: 36 operands: 11
10	Operation	operator: 12 operands: 13
11	ExprTuple	14, 40
12	Literal
13	ExprTuple	15, 16
14	Operation	operator: 25 operands: 17
15	Operation	operator: 25 operands: 18
16	Operation	operator: 36 operands: 19
17	ExprTuple	20, 21
18	ExprTuple	22, 35
19	ExprTuple	40, 23
20	Variable
21	Operation	operator: 31 operand: 27
22	Variable
23	Operation	operator: 25 operands: 26
24	ExprTuple	27
25	Literal
26	ExprTuple	41, 28
27	Operation	operator: 29 operands: 30
28	Operation	operator: 31 operand: 35
29	Literal
30	ExprTuple	33, 34
31	Literal
32	ExprTuple	35
33	Operation	operator: 36 operands: 37
34	Operation	operator: 38 operand: 42
35	Literal
36	Literal
37	ExprTuple	40, 41
38	Literal
39	ExprTuple	42
40	Literal
41	Literal
42	Literal