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
expr = Equals(VecAdd(TensorProd(x, y, z), TensorProd(x, y, w), TensorProd(x, y, v)), VecAdd(TensorProd(x, TensorProd(y, z)), TensorProd(x, TensorProd(y, w)), TensorProd(x, TensorProd(y, v))))

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} \left(y {\otimes} v\right)\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, 10
6	Literal
7	ExprTuple	11, 12, 13
8	Operation	operator: 26 operands: 14
9	Operation	operator: 26 operands: 15
10	Operation	operator: 26 operands: 16
11	Operation	operator: 26 operands: 17
12	Operation	operator: 26 operands: 18
13	Operation	operator: 26 operands: 19
14	ExprTuple	22, 30, 28
15	ExprTuple	22, 30, 29
16	ExprTuple	22, 30, 31
17	ExprTuple	22, 20
18	ExprTuple	22, 21
19	ExprTuple	22, 23
20	Operation	operator: 26 operands: 24
21	Operation	operator: 26 operands: 25
22	Variable
23	Operation	operator: 26 operands: 27
24	ExprTuple	30, 28
25	ExprTuple	30, 29
26	Literal
27	ExprTuple	30, 31
28	Variable
29	Variable
30	Variable
31	Variable