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

# build up the expression from sub-expressions
expr = Lambda(l, Conditional(InSet(frac(one, Exp(_diff_l_scaled_delta_floor, two)), Complex), InSet(l, _neg_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}} \in \mathbb{C} \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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