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 ExprRange, ExprTuple, IndexedVar, Variable, a, c, l
from proveit.logic import Equals, Forall, 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 = Add(l, one)
sub_expr4 = IndexedVar(c, one)
sub_expr5 = ExprRange(sub_expr1, IndexedVar(a, sub_expr1), one, zero)
expr = ExprTuple(Forall(instance_param_or_params = sub_expr2, instance_expr = InSet(sub_expr3, Complex), domain = Integer), Forall(instance_param_or_params = [sub_expr5, sub_expr4], instance_expr = Equals(Mult(sub_expr5, Sum(index_or_indices = sub_expr2, summand = sub_expr3, domain = Integer), sub_expr4), Sum(index_or_indices = sub_expr2, summand = Mult(sub_expr5, sub_expr3, sub_expr4), domain = Integer)).with_wrapping_at(2), domain = Complex).with_wrapping())

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(\forall_{l \in \mathbb{Z}}~\left(\left(l + 1\right) \in \mathbb{C}\right), \begin{array}{l}\forall_{a_{1}, a_{2}, \ldots, a_{0}, c_{1} \in \mathbb{C}}~\\
\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}\right)\end{array}\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 4 operand: 6
2	Operation	operator: 4 operand: 7
3	ExprTuple	6
4	Literal
5	ExprTuple	7
6	Lambda	parameter: 55 body: 8
7	Lambda	parameters: 9 body: 10
8	Conditional	value: 11 condition: 41
9	ExprTuple	42, 44
10	Conditional	value: 12 condition: 13
11	Operation	operator: 45 operands: 14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operands: 18
14	ExprTuple	43, 36
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21, 22
19	Operation	operator: 39 operands: 23
20	Operation	operator: 30 operand: 28
21	ExprRange	lambda_map: 25 start_index: 56 end_index: 48
22	Operation	operator: 45 operands: 26
23	ExprTuple	42, 27, 44
24	ExprTuple	28
25	Lambda	parameter: 59 body: 29
26	ExprTuple	44, 36
27	Operation	operator: 30 operand: 34
28	Lambda	parameter: 55 body: 32
29	Operation	operator: 45 operands: 33
30	Literal
31	ExprTuple	34
32	Conditional	value: 35 condition: 41
33	ExprTuple	54, 36
34	Lambda	parameter: 55 body: 38
35	Operation	operator: 39 operands: 40
36	Literal
37	ExprTuple	55
38	Conditional	value: 43 condition: 41
39	Literal
40	ExprTuple	42, 43, 44
41	Operation	operator: 45 operands: 46
42	ExprRange	lambda_map: 47 start_index: 56 end_index: 48
43	Operation	operator: 49 operands: 50
44	IndexedVar	variable: 51 index: 56
45	Literal
46	ExprTuple	55, 53
47	Lambda	parameter: 59 body: 54
48	Literal
49	Literal
50	ExprTuple	55, 56
51	Variable
52	ExprTuple	56
53	Literal
54	IndexedVar	variable: 57 index: 59
55	Variable
56	Literal
57	Variable
58	ExprTuple	59
59	Variable