Expression of type Equals

from the theory of proveit.linear_algebra.addition

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 v, w, x, y, z
from proveit.linear_algebra import TensorProd, VecAdd
from proveit.logic import Equals

# build up the expression from sub-expressions
sub_expr1 = TensorProd(x, y, v)
expr = Equals(VecAdd(TensorProd(x, y, z), TensorProd(x, y, w), sub_expr1), VecAdd(TensorProd(x, TensorProd(y, z)), TensorProd(x, TensorProd(y, w)), sub_expr1))

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(\left(x {\otimes} y {\otimes} z\right) + \left(x {\otimes} y {\otimes} w\right) + \left(x {\otimes} y {\otimes} v\right)\right) = \left(\left(x {\otimes} \left(y {\otimes} z\right)\right) + \left(x {\otimes} \left(y {\otimes} w\right)\right) + \left(x {\otimes} y {\otimes} v\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 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9, 12
6	Literal
7	ExprTuple	10, 11, 12
8	Operation	operator: 23 operands: 13
9	Operation	operator: 23 operands: 14
10	Operation	operator: 23 operands: 15
11	Operation	operator: 23 operands: 16
12	Operation	operator: 23 operands: 17
13	ExprTuple	20, 26, 25
14	ExprTuple	20, 26, 27
15	ExprTuple	20, 18
16	ExprTuple	20, 19
17	ExprTuple	20, 26, 21
18	Operation	operator: 23 operands: 22
19	Operation	operator: 23 operands: 24
20	Variable
21	Variable
22	ExprTuple	26, 25
23	Literal
24	ExprTuple	26, 27
25	Variable
26	Variable
27	Variable