Expression of type Lambda

from the theory of proveit.numbers.summation

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 Add, Complex, Integer, Mult, Sum, one, zero

# 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 = Add(l, one)
sub_expr6 = ExprRange(sub_expr1, sub_expr4, one, zero)
expr = Lambda([sub_expr3, sub_expr6], Conditional(Equals(Mult(sub_expr3, Sum(index_or_indices = sub_expr2, summand = sub_expr5, domain = Integer), sub_expr6), Sum(index_or_indices = sub_expr2, summand = Mult(sub_expr3, sub_expr5, sub_expr6), domain = Integer)).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 \in \mathbb{Z}}~\left(l + 1\right)\right]\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{0}\right) =  \\ \left[\sum_{l \in \mathbb{Z}}~\left(a_{1} \cdot \left(l + 1\right)\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	32, 34
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: 29 operands: 13
10	Operation	operator: 20 operand: 18
11	Operation	operator: 35 operands: 15
12	ExprRange	lambda_map: 16 start_index: 45 end_index: 42
13	ExprTuple	32, 17, 34
14	ExprTuple	18
15	ExprTuple	32, 26
16	Lambda	parameter: 49 body: 19
17	Operation	operator: 20 operand: 24
18	Lambda	parameter: 44 body: 22
19	Operation	operator: 35 operands: 23
20	Literal
21	ExprTuple	24
22	Conditional	value: 25 condition: 31
23	ExprTuple	46, 26
24	Lambda	parameter: 44 body: 28
25	Operation	operator: 29 operands: 30
26	Literal
27	ExprTuple	44
28	Conditional	value: 33 condition: 31
29	Literal
30	ExprTuple	32, 33, 34
31	Operation	operator: 35 operands: 36
32	IndexedVar	variable: 37 index: 45
33	Operation	operator: 39 operands: 40
34	ExprRange	lambda_map: 41 start_index: 45 end_index: 42
35	Literal
36	ExprTuple	44, 43
37	Variable
38	ExprTuple	45
39	Literal
40	ExprTuple	44, 45
41	Lambda	parameter: 49 body: 46
42	Literal
43	Literal
44	Variable
45	Literal
46	IndexedVar	variable: 47 index: 49
47	Variable
48	ExprTuple	49
49	Variable