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.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 Mult

# build up the expression from sub-expressions
expr = Equals(Mult(a_1_to_i, b_1_to_j, c_1_to_k), Mult(a_1_to_i, Mult(b_1_to_j), c_1_to_k)).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 b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j}\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right) =  \\ \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot \left(b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j}\right)\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\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: 12 operands: 5
4	Operation	operator: 12 operands: 6
5	ExprTuple	7, 17, 9
6	ExprTuple	7, 8, 9
7	ExprRange	lambda_map: 10 start_index: 21 end_index: 11
8	Operation	operator: 12 operands: 13
9	ExprRange	lambda_map: 14 start_index: 21 end_index: 15
10	Lambda	parameter: 27 body: 16
11	Variable
12	Literal
13	ExprTuple	17
14	Lambda	parameter: 27 body: 18
15	Variable
16	IndexedVar	variable: 19 index: 27
17	ExprRange	lambda_map: 20 start_index: 21 end_index: 22
18	IndexedVar	variable: 23 index: 27
19	Variable
20	Lambda	parameter: 27 body: 24
21	Literal
22	Variable
23	Variable
24	IndexedVar	variable: 25 index: 27
25	Variable
26	ExprTuple	27
27	Variable