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, sub_expr1)
sub_expr4 = IndexedVar(c, one)
sub_expr5 = Add(l, one)
sub_expr6 = ExprRange(sub_expr1, sub_expr3, one, zero)
expr = Lambda([sub_expr6, sub_expr4], Conditional(Equals(Mult(sub_expr6, Sum(index_or_indices = sub_expr2, summand = sub_expr5, domain = Integer), sub_expr4), Sum(index_or_indices = sub_expr2, summand = Mult(sub_expr6, sub_expr5, sub_expr4), domain = Integer)).with_wrapping_at(2), And(ExprRange(sub_expr1, InSet(sub_expr3, Complex), one, zero), InSet(sub_expr4, Complex))))

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}, a_{2}, \ldots, a_{0}, c_{1}\right) \mapsto \left\{\begin{array}{c} \begin{array}{l} \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{0} \cdot \left[\sum_{l \in \mathbb{Z}}~\left(l + 1\right)\right] \cdot c_{1}\right) =  \\ \left[\sum_{l \in \mathbb{Z}}~\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{0} \cdot \left(l + 1\right) \cdot c_{1}\right)\right] \end{array} \end{array} \textrm{ if } \left(a_{1} \in \mathbb{C}\right) ,  \left(a_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(a_{0} \in \mathbb{C}\right) ,  c_{1} \in \mathbb{C}\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	ExprRange	lambda_map: 15 start_index: 46 end_index: 38
12	Operation	operator: 35 operands: 16
13	ExprTuple	32, 17, 34
14	ExprTuple	18
15	Lambda	parameter: 49 body: 19
16	ExprTuple	34, 26
17	Operation	operator: 20 operand: 24
18	Lambda	parameter: 45 body: 22
19	Operation	operator: 35 operands: 23
20	Literal
21	ExprTuple	24
22	Conditional	value: 25 condition: 31
23	ExprTuple	44, 26
24	Lambda	parameter: 45 body: 28
25	Operation	operator: 29 operands: 30
26	Literal
27	ExprTuple	45
28	Conditional	value: 33 condition: 31
29	Literal
30	ExprTuple	32, 33, 34
31	Operation	operator: 35 operands: 36
32	ExprRange	lambda_map: 37 start_index: 46 end_index: 38
33	Operation	operator: 39 operands: 40
34	IndexedVar	variable: 41 index: 46
35	Literal
36	ExprTuple	45, 43
37	Lambda	parameter: 49 body: 44
38	Literal
39	Literal
40	ExprTuple	45, 46
41	Variable
42	ExprTuple	46
43	Literal
44	IndexedVar	variable: 47 index: 49
45	Variable
46	Literal
47	Variable
48	ExprTuple	49
49	Variable