Expression of type Conditional

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, ExprRange, IndexedVar, Variable, a, c, l
from proveit.logic import And, Equals, InSet
from proveit.numbers import Complex, Exp, Mult, Sum, frac, one, two, zero
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _pos_domain

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = [l]
sub_expr3 = IndexedVar(a, one)
sub_expr4 = IndexedVar(c, sub_expr1)
sub_expr5 = ExprRange(sub_expr1, sub_expr4, one, zero)
sub_expr6 = frac(one, Exp(_diff_l_scaled_delta_floor, two))
expr = Conditional(Equals(Mult(sub_expr3, Sum(index_or_indices = sub_expr2, summand = sub_expr6, domain = _pos_domain), sub_expr5), Sum(index_or_indices = sub_expr2, summand = Mult(sub_expr3, sub_expr6, sub_expr5), domain = _pos_domain)).with_wrapping_at(2), And(InSet(sub_expr3, Complex), ExprRange(sub_expr1, InSet(sub_expr4, Complex), one, 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\{\begin{array}{c} \begin{array}{l} \left(a_{1} \cdot \left(\sum_{l = e + 1}^{2^{t - 1}} \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\right)\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{0}\right) =  \\ \left(\sum_{l = e + 1}^{2^{t - 1}} \left(a_{1} \cdot \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{0}\right)\right) \end{array} \end{array} \textrm{ if } a_{1} \in \mathbb{C}, \left(c_{1} \in \mathbb{C}\right) ,  \left(c_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(c_{0} \in \mathbb{C}\right)\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10
7	Operation	operator: 65 operands: 11
8	Operation	operator: 18 operand: 16
9	Operation	operator: 32 operands: 13
10	ExprRange	lambda_map: 14 start_index: 67 end_index: 38
11	ExprTuple	29, 15, 31
12	ExprTuple	16
13	ExprTuple	29, 24
14	Lambda	parameter: 50 body: 17
15	Operation	operator: 18 operand: 22
16	Lambda	parameter: 56 body: 20
17	Operation	operator: 32 operands: 21
18	Literal
19	ExprTuple	22
20	Conditional	value: 23 condition: 28
21	ExprTuple	41, 24
22	Lambda	parameter: 56 body: 26
23	Operation	operator: 65 operands: 27
24	Literal
25	ExprTuple	56
26	Conditional	value: 30 condition: 28
27	ExprTuple	29, 30, 31
28	Operation	operator: 32 operands: 33
29	IndexedVar	variable: 34 index: 67
30	Operation	operator: 35 operands: 36
31	ExprRange	lambda_map: 37 start_index: 67 end_index: 38
32	Literal
33	ExprTuple	56, 39
34	Variable
35	Literal
36	ExprTuple	67, 40
37	Lambda	parameter: 50 body: 41
38	Literal
39	Operation	operator: 42 operands: 43
40	Operation	operator: 70 operands: 44
41	IndexedVar	variable: 45 index: 50
42	Literal
43	ExprTuple	47, 48
44	ExprTuple	49, 74
45	Variable
46	ExprTuple	50
47	Operation	operator: 58 operands: 51
48	Operation	operator: 70 operands: 52
49	Operation	operator: 58 operands: 53
50	Variable
51	ExprTuple	54, 67
52	ExprTuple	74, 55
53	ExprTuple	56, 57
54	Variable
55	Operation	operator: 58 operands: 59
56	Variable
57	Operation	operator: 63 operand: 62
58	Literal
59	ExprTuple	75, 61
60	ExprTuple	62
61	Operation	operator: 63 operand: 67
62	Operation	operator: 65 operands: 66
63	Literal
64	ExprTuple	67
65	Literal
66	ExprTuple	68, 69
67	Literal
68	Operation	operator: 70 operands: 71
69	Operation	operator: 72 operand: 76
70	Literal
71	ExprTuple	74, 75
72	Literal
73	ExprTuple	76
74	Literal
75	Literal
76	Literal