Expression of type Forall

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 ExprRange, IndexedVar, Variable, a, c, l
from proveit.logic import Equals, Forall
from proveit.numbers import Complex, Exp, Mult, Sum, frac, one, two, zero
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _neg_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 = ExprRange(sub_expr1, IndexedVar(c, sub_expr1), one, zero)
sub_expr5 = frac(one, Exp(_diff_l_scaled_delta_floor, two))
expr = Forall(instance_param_or_params = [sub_expr3, sub_expr4], instance_expr = Equals(Mult(sub_expr3, Sum(index_or_indices = sub_expr2, summand = sub_expr5, domain = _neg_domain), sub_expr4), Sum(index_or_indices = sub_expr2, summand = Mult(sub_expr3, sub_expr5, sub_expr4), domain = _neg_domain)).with_wrapping_at(2), domain = Complex).with_wrapping()

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())

\begin{array}{l}\forall_{a_{1}, c_{1}, c_{2}, \ldots, c_{0} \in \mathbb{C}}~\\
\left(\begin{array}{c} \begin{array}{l} \left(a_{1} \cdot \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)\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{0}\right) =  \\ \left(\sum_{l = -2^{t - 1} + 1}^{-\left(e + 1\right)} \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}\right)\end{array}

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	True	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 4 body: 5
4	ExprTuple	34, 36
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	14, 15
12	Operation	operator: 70 operands: 16
13	Operation	operator: 23 operand: 21
14	Operation	operator: 37 operands: 18
15	ExprRange	lambda_map: 19 start_index: 87 end_index: 43
16	ExprTuple	34, 20, 36
17	ExprTuple	21
18	ExprTuple	34, 29
19	Lambda	parameter: 55 body: 22
20	Operation	operator: 23 operand: 27
21	Lambda	parameter: 61 body: 25
22	Operation	operator: 37 operands: 26
23	Literal
24	ExprTuple	27
25	Conditional	value: 28 condition: 33
26	ExprTuple	46, 29
27	Lambda	parameter: 61 body: 31
28	Operation	operator: 70 operands: 32
29	Literal
30	ExprTuple	61
31	Conditional	value: 35 condition: 33
32	ExprTuple	34, 35, 36
33	Operation	operator: 37 operands: 38
34	IndexedVar	variable: 39 index: 87
35	Operation	operator: 40 operands: 41
36	ExprRange	lambda_map: 42 start_index: 87 end_index: 43
37	Literal
38	ExprTuple	61, 44
39	Variable
40	Literal
41	ExprTuple	87, 45
42	Lambda	parameter: 55 body: 46
43	Literal
44	Operation	operator: 47 operands: 48
45	Operation	operator: 77 operands: 49
46	IndexedVar	variable: 50 index: 55
47	Literal
48	ExprTuple	52, 53
49	ExprTuple	54, 82
50	Variable
51	ExprTuple	55
52	Operation	operator: 75 operands: 56
53	Operation	operator: 85 operand: 60
54	Operation	operator: 75 operands: 58
55	Variable
56	ExprTuple	59, 87
57	ExprTuple	60
58	ExprTuple	61, 62
59	Operation	operator: 85 operand: 66
60	Operation	operator: 75 operands: 64
61	Variable
62	Operation	operator: 85 operand: 68
63	ExprTuple	66
64	ExprTuple	67, 87
65	ExprTuple	68
66	Operation	operator: 77 operands: 69
67	Variable
68	Operation	operator: 70 operands: 71
69	ExprTuple	82, 72
70	Literal
71	ExprTuple	73, 74
72	Operation	operator: 75 operands: 76
73	Operation	operator: 77 operands: 78
74	Operation	operator: 79 operand: 84
75	Literal
76	ExprTuple	83, 81
77	Literal
78	ExprTuple	82, 83
79	Literal
80	ExprTuple	84
81	Operation	operator: 85 operand: 87
82	Literal
83	Literal
84	Literal
85	Literal
86	ExprTuple	87
87	Literal