Expression of type LessEq

from the theory of proveit.numbers.absolute_value

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, b, c, n, x
from proveit.core_expr_types import x_1_to_n
from proveit.numbers import Abs, Add, LessEq, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = LessEq(Abs(Add(a, b, x_1_to_n, c)), Add(Abs(a), Abs(b), ExprRange(sub_expr1, Abs(IndexedVar(x, sub_expr1)), one, n), Abs(c)))

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|a + b+ x_{1} +  x_{2} +  \ldots +  x_{n} + c\right| \leq \left(\left|a\right| + \left|b\right|+ \left|x_{1}\right| +  \left|x_{2}\right| +  \ldots +  \left|x_{n}\right| + \left|c\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: 26 operand: 7
4	Operation	operator: 12 operands: 6
5	ExprTuple	7
6	ExprTuple	8, 9, 10, 11
7	Operation	operator: 12 operands: 13
8	Operation	operator: 26 operand: 19
9	Operation	operator: 26 operand: 20
10	ExprRange	lambda_map: 16 start_index: 24 end_index: 25
11	Operation	operator: 26 operand: 22
12	Literal
13	ExprTuple	19, 20, 18, 22
14	ExprTuple	19
15	ExprTuple	20
16	Lambda	parameter: 31 body: 21
17	ExprTuple	22
18	ExprRange	lambda_map: 23 start_index: 24 end_index: 25
19	Variable
20	Variable
21	Operation	operator: 26 operand: 28
22	Variable
23	Lambda	parameter: 31 body: 28
24	Literal
25	Variable
26	Literal
27	ExprTuple	28
28	IndexedVar	variable: 29 index: 31
29	Variable
30	ExprTuple	31
31	Variable