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, ExprRange, IndexedVar, Lambda, Variable, a, c, l
from proveit.logic import InSet
from proveit.numbers import Exp, Mult, frac, one, two, zero
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _pos_domain

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda(l, Conditional(Mult(IndexedVar(a, one), frac(one, Exp(_diff_l_scaled_delta_floor, two)), ExprRange(sub_expr1, IndexedVar(c, sub_expr1), one, zero)), 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\{a_{1} \cdot \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{0} \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: 35 body: 2
1	ExprTuple	35
2	Conditional	value: 3 condition: 4
3	Operation	operator: 43 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9, 10
6	Literal
7	ExprTuple	35, 11
8	IndexedVar	variable: 12 index: 42
9	Operation	operator: 13 operands: 14
10	ExprRange	lambda_map: 15 start_index: 42 end_index: 16
11	Operation	operator: 17 operands: 18
12	Variable
13	Literal
14	ExprTuple	42, 19
15	Lambda	parameter: 29 body: 20
16	Literal
17	Literal
18	ExprTuple	21, 22
19	Operation	operator: 47 operands: 23
20	IndexedVar	variable: 24 index: 29
21	Operation	operator: 33 operands: 26
22	Operation	operator: 47 operands: 27
23	ExprTuple	28, 51
24	Variable
25	ExprTuple	29
26	ExprTuple	30, 42
27	ExprTuple	51, 31
28	Operation	operator: 33 operands: 32
29	Variable
30	Variable
31	Operation	operator: 33 operands: 34
32	ExprTuple	35, 36
33	Literal
34	ExprTuple	52, 37
35	Variable
36	Operation	operator: 39 operand: 41
37	Operation	operator: 39 operand: 42
38	ExprTuple	41
39	Literal
40	ExprTuple	42
41	Operation	operator: 43 operands: 44
42	Literal
43	Literal
44	ExprTuple	45, 46
45	Operation	operator: 47 operands: 48
46	Operation	operator: 49 operand: 53
47	Literal
48	ExprTuple	51, 52
49	Literal
50	ExprTuple	53
51	Literal
52	Literal
53	Literal