Expression of type Equals

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, IndexedVar, Variable, a, c, l
from proveit.logic import Equals
from proveit.numbers import Add, 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 = 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)

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())

\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}

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	(2)	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

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