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, b, l
from proveit.logic import And, InSet, NotEquals, NotInSet, Set
from proveit.numbers import Integer, frac, subtract, zero
from proveit.physics.quantum.QPE import _b_floor, _b_round, _delta_b, _full_domain, _two_pow_t

# build up the expression from sub-expressions
expr = Lambda([b, l], Conditional(NotInSet(subtract(_delta_b, frac(l, _two_pow_t)), Integer), And(InSet(b, Set(_b_floor, _b_round)), InSet(l, _full_domain), NotEquals(l, zero))))

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())

\left(b, l\right) \mapsto \left\{\left(\delta_{b} - \frac{l}{2^{t}}\right) \notin \mathbb{Z} \textrm{ if } b \in \left\{b_{\textit{f}}, b_{\textit{r}}\right\} ,  l \in \{-2^{t - 1} + 1~\ldotp \ldotp~2^{t - 1}\} ,  l \neq 0\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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