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, ExprRange, IndexedVar, Lambda, 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 = Lambda([sub_expr3, sub_expr5], 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(a_{1}, c_{1}, c_{2}, \ldots, c_{0}\right) \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

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