Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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(\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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	33, 35
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13
10	Operation	operator: 30 operands: 14
11	Operation	operator: 21 operand: 19
12	Operation	operator: 36 operands: 16
13	ExprRange	lambda_map: 17 start_index: 46 end_index: 43
14	ExprTuple	33, 18, 35
15	ExprTuple	19
16	ExprTuple	33, 27
17	Lambda	parameter: 50 body: 20
18	Operation	operator: 21 operand: 25
19	Lambda	parameter: 45 body: 23
20	Operation	operator: 36 operands: 24
21	Literal
22	ExprTuple	25
23	Conditional	value: 26 condition: 32
24	ExprTuple	47, 27
25	Lambda	parameter: 45 body: 29
26	Operation	operator: 30 operands: 31
27	Literal
28	ExprTuple	45
29	Conditional	value: 34 condition: 32
30	Literal
31	ExprTuple	33, 34, 35
32	Operation	operator: 36 operands: 37
33	IndexedVar	variable: 38 index: 46
34	Operation	operator: 40 operands: 41
35	ExprRange	lambda_map: 42 start_index: 46 end_index: 43
36	Literal
37	ExprTuple	45, 44
38	Variable
39	ExprTuple	46
40	Literal
41	ExprTuple	45, 46
42	Lambda	parameter: 50 body: 47
43	Literal
44	Literal
45	Variable
46	Literal
47	IndexedVar	variable: 48 index: 50
48	Variable
49	ExprTuple	50
50	Variable