Expression of type Less

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 l, m, n
from proveit.numbers import Interval, Less, Sum
from proveit.numbers.summation import al, bl

# build up the expression from sub-expressions
sub_expr1 = [l]
sub_expr2 = Interval(m, n)
expr = Less(Sum(index_or_indices = sub_expr1, summand = al, domain = sub_expr2), Sum(index_or_indices = sub_expr1, summand = bl, domain = sub_expr2))

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(\sum_{l = m}^{n} a\left(l\right)\right) < \left(\sum_{l = m}^{n} b\left(l\right)\right)

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.	()	()	('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: 6 operand: 8
4	Operation	operator: 6 operand: 9
5	ExprTuple	8
6	Literal
7	ExprTuple	9
8	Lambda	parameter: 20 body: 10
9	Lambda	parameter: 20 body: 11
10	Conditional	value: 12 condition: 14
11	Conditional	value: 13 condition: 14
12	Operation	operator: 15 operand: 20
13	Operation	operator: 16 operand: 20
14	Operation	operator: 18 operands: 19
15	Variable
16	Variable
17	ExprTuple	20
18	Literal
19	ExprTuple	20, 21
20	Variable
21	Operation	operator: 22 operands: 23
22	Literal
23	ExprTuple	24, 25
24	Variable
25	Variable