Expression of type Equals

from the theory of proveit.linear_algebra.tensors

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, x
from proveit.linear_algebra import TensorProd
from proveit.logic import Equals
from proveit.numbers import one, three, two

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

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} {\otimes}  x_{2} {\otimes}  \ldots {\otimes}  x_{3}\right) = \left(x_{1} {\otimes} x_{2} {\otimes} x_{3}\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
6	Literal
7	ExprTuple	9, 10, 11
8	ExprRange	lambda_map: 12 start_index: 17 end_index: 19
9	IndexedVar	variable: 20 index: 17
10	IndexedVar	variable: 20 index: 18
11	IndexedVar	variable: 20 index: 19
12	Lambda	parameter: 22 body: 16
13	ExprTuple	17
14	ExprTuple	18
15	ExprTuple	19
16	IndexedVar	variable: 20 index: 22
17	Literal
18	Literal
19	Literal
20	Variable
21	ExprTuple	22
22	Variable