Expression of type Equals

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, n, x
from proveit.core_expr_types import x_1_to_n
from proveit.logic import Equals
from proveit.numbers import Abs, Mult, one

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

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|x_{1} \cdot  x_{2} \cdot  \ldots \cdot  x_{n}\right| = \left(\left|x_{1}\right| \cdot  \left|x_{2}\right| \cdot  \ldots \cdot  \left|x_{n}\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: 17 operand: 7
4	Operation	operator: 9 operands: 6
5	ExprTuple	7
6	ExprTuple	8
7	Operation	operator: 9 operands: 10
8	ExprRange	lambda_map: 11 start_index: 15 end_index: 16
9	Literal
10	ExprTuple	12
11	Lambda	parameter: 22 body: 13
12	ExprRange	lambda_map: 14 start_index: 15 end_index: 16
13	Operation	operator: 17 operand: 19
14	Lambda	parameter: 22 body: 19
15	Literal
16	Variable
17	Literal
18	ExprTuple	19
19	IndexedVar	variable: 20 index: 22
20	Variable
21	ExprTuple	22
22	Variable