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, e, l
from proveit.logic import InSet
from proveit.numbers import Add, Exp, LessEq, Mult, Sum, four, frac, one, two
from proveit.physics.quantum.QPE import Pfail, _diff_l_scaled_delta_floor, _e_domain, _neg_domain, _pos_domain

# build up the expression from sub-expressions
sub_expr1 = [l]
sub_expr2 = frac(one, Exp(_diff_l_scaled_delta_floor, two))
expr = ExprTuple(Lambda(e, Conditional(LessEq(Pfail(e), Mult(frac(one, four), Add(Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = _neg_domain), Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = _pos_domain)))), InSet(e, _e_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())

\left(e \mapsto \left\{\left[P_{\rm fail}\right]\left(e\right) \leq \left(\frac{1}{4} \cdot \left(\left(\sum_{l = -2^{t - 1} + 1}^{-\left(e + 1\right)} \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\right) + \left(\sum_{l = e + 1}^{2^{t - 1}} \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\right)\right)\right) \textrm{ if } e \in \{1~\ldotp \ldotp~2^{t - 1} - 2\}\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	parameter: 63 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 40 operands: 7
5	Literal
6	ExprTuple	8, 9
7	ExprTuple	63, 10
8	Operation	operator: 11 operand: 63
9	Operation	operator: 66 operands: 13
10	Operation	operator: 47 operands: 14
11	Literal
12	ExprTuple	63
13	ExprTuple	15, 16
14	ExprTuple	83, 17
15	Operation	operator: 38 operands: 18
16	Operation	operator: 71 operands: 19
17	Operation	operator: 71 operands: 20
18	ExprTuple	83, 21
19	ExprTuple	22, 23
20	ExprTuple	62, 24
21	Literal
22	Operation	operator: 26 operand: 29
23	Operation	operator: 26 operand: 30
24	Operation	operator: 81 operand: 78
25	ExprTuple	29
26	Literal
27	ExprTuple	30
28	ExprTuple	78
29	Lambda	parameter: 57 body: 31
30	Lambda	parameter: 57 body: 33
31	Conditional	value: 35 condition: 34
32	ExprTuple	57
33	Conditional	value: 35 condition: 36
34	Operation	operator: 40 operands: 37
35	Operation	operator: 38 operands: 39
36	Operation	operator: 40 operands: 41
37	ExprTuple	57, 42
38	Literal
39	ExprTuple	83, 43
40	Literal
41	ExprTuple	57, 44
42	Operation	operator: 47 operands: 45
43	Operation	operator: 73 operands: 46
44	Operation	operator: 47 operands: 48
45	ExprTuple	49, 50
46	ExprTuple	51, 78
47	Literal
48	ExprTuple	56, 62
49	Operation	operator: 71 operands: 52
50	Operation	operator: 81 operand: 56
51	Operation	operator: 71 operands: 54
52	ExprTuple	55, 83
53	ExprTuple	56
54	ExprTuple	57, 58
55	Operation	operator: 81 operand: 62
56	Operation	operator: 71 operands: 60
57	Variable
58	Operation	operator: 81 operand: 64
59	ExprTuple	62
60	ExprTuple	63, 83
61	ExprTuple	64
62	Operation	operator: 73 operands: 65
63	Variable
64	Operation	operator: 66 operands: 67
65	ExprTuple	78, 68
66	Literal
67	ExprTuple	69, 70
68	Operation	operator: 71 operands: 72
69	Operation	operator: 73 operands: 74
70	Operation	operator: 75 operand: 80
71	Literal
72	ExprTuple	79, 77
73	Literal
74	ExprTuple	78, 79
75	Literal
76	ExprTuple	80
77	Operation	operator: 81 operand: 83
78	Literal
79	Literal
80	Literal
81	Literal
82	ExprTuple	83
83	Literal