Expression of type Equals

from the theory of proveit.numbers.multiplication

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, b, j
from proveit.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k
from proveit.logic import Equals
from proveit.numbers import Abs, Add, Mult, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
expr = Equals(Mult(a_1_to_i, Abs(Add(b_1_to_j)), c_1_to_k), Abs(Add(ExprRange(sub_expr1, Mult(a_1_to_i, IndexedVar(b, sub_expr1), c_1_to_k), one, j)))).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_{i} \cdot \left|b_{1} +  b_{2} +  \ldots +  b_{j}\right|\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right) =  \\ \left|\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot b_{1}\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right) +  \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot b_{2}\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right) +  \ldots +  \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot b_{j}\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\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: 21 operands: 5
4	Operation	operator: 9 operand: 8
5	ExprTuple	24, 7, 26
6	ExprTuple	8
7	Operation	operator: 9 operand: 12
8	Operation	operator: 14 operands: 11
9	Literal
10	ExprTuple	12
11	ExprTuple	13
12	Operation	operator: 14 operands: 15
13	ExprRange	lambda_map: 16 start_index: 32 end_index: 20
14	Literal
15	ExprTuple	17
16	Lambda	parameter: 35 body: 18
17	ExprRange	lambda_map: 19 start_index: 32 end_index: 20
18	Operation	operator: 21 operands: 22
19	Lambda	parameter: 40 body: 23
20	Variable
21	Literal
22	ExprTuple	24, 25, 26
23	IndexedVar	variable: 29 index: 40
24	ExprRange	lambda_map: 27 start_index: 32 end_index: 28
25	IndexedVar	variable: 29 index: 35
26	ExprRange	lambda_map: 31 start_index: 32 end_index: 33
27	Lambda	parameter: 40 body: 34
28	Variable
29	Variable
30	ExprTuple	35
31	Lambda	parameter: 40 body: 36
32	Literal
33	Variable
34	IndexedVar	variable: 37 index: 40
35	Variable
36	IndexedVar	variable: 38 index: 40
37	Variable
38	Variable
39	ExprTuple	40
40	Variable