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 IntervalCO, Neg, frac, one, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _full_domain, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = frac(one, two)
expr = Lambda(l, Conditional(InSet(subtract(_delta_b_floor, frac(l, _two_pow_t)), IntervalCO(Neg(sub_expr1), sub_expr1)), InSet(l, _full_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(\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\right) \in \left[-\frac{1}{2},\frac{1}{2}\right) \textrm{ if } l \in \{-2^{t - 1} + 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: 33 body: 2
1	ExprTuple	33
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	33, 10
8	Operation	operator: 41 operands: 11
9	Operation	operator: 12 operands: 13
10	Operation	operator: 14 operands: 15
11	ExprTuple	16, 17
12	Literal
13	ExprTuple	18, 27
14	Literal
15	ExprTuple	19, 35
16	Operation	operator: 20 operand: 25
17	Operation	operator: 45 operand: 26
18	Operation	operator: 45 operand: 27
19	Operation	operator: 41 operands: 24
20	Literal
21	ExprTuple	25
22	ExprTuple	26
23	ExprTuple	27
24	ExprTuple	28, 47
25	Literal
26	Operation	operator: 30 operands: 29
27	Operation	operator: 30 operands: 31
28	Operation	operator: 45 operand: 35
29	ExprTuple	33, 34
30	Literal
31	ExprTuple	47, 39
32	ExprTuple	35
33	Variable
34	Operation	operator: 37 operands: 36
35	Operation	operator: 37 operands: 38
36	ExprTuple	39, 43
37	Literal
38	ExprTuple	39, 40
39	Literal
40	Operation	operator: 41 operands: 42
41	Literal
42	ExprTuple	43, 44
43	Literal
44	Operation	operator: 45 operand: 47
45	Literal
46	ExprTuple	47
47	Literal