Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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(\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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	33, 41
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13, 14
10	Operation	operator: 51 operands: 15
11	Literal
12	Operation	operator: 17 operands: 16
13	Operation	operator: 17 operands: 18
14	Operation	operator: 19 operands: 20
15	ExprTuple	21, 22
16	ExprTuple	33, 23
17	Literal
18	ExprTuple	41, 24
19	Literal
20	ExprTuple	41, 25
21	Operation	operator: 26 operand: 33
22	Operation	operator: 55 operand: 34
23	Operation	operator: 29 operands: 30
24	Operation	operator: 31 operands: 32
25	Literal
26	Literal
27	ExprTuple	33
28	ExprTuple	34
29	Literal
30	ExprTuple	35, 36
31	Literal
32	ExprTuple	37, 46
33	Variable
34	Operation	operator: 38 operands: 39
35	Literal
36	Literal
37	Operation	operator: 51 operands: 40
38	Literal
39	ExprTuple	41, 42
40	ExprTuple	43, 57
41	Variable
42	Operation	operator: 47 operands: 44
43	Operation	operator: 55 operand: 46
44	ExprTuple	49, 53
45	ExprTuple	46
46	Operation	operator: 47 operands: 48
47	Literal
48	ExprTuple	49, 50
49	Literal
50	Operation	operator: 51 operands: 52
51	Literal
52	ExprTuple	53, 54
53	Literal
54	Operation	operator: 55 operand: 57
55	Literal
56	ExprTuple	57
57	Literal