Expression of type Conditional

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

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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