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 fi, i, u, v, w, x, z
from proveit.linear_algebra import TensorProd, VecSum
from proveit.logic import Equals
from proveit.numbers import Interval, five, one

# build up the expression from sub-expressions
sub_expr1 = [i]
sub_expr2 = Interval(one, five)
expr = Equals(TensorProd(u, v, w, x, VecSum(index_or_indices = sub_expr1, summand = fi, domain = sub_expr2), z), VecSum(index_or_indices = sub_expr1, summand = TensorProd(u, v, w, x, fi, z), domain = sub_expr2))

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(u {\otimes} v {\otimes} w {\otimes} x {\otimes} \left(\sum_{i=1}^{5} f\left(i\right)\right) {\otimes} z\right) = \left(\sum_{i=1}^{5} \left(u {\otimes} v {\otimes} w {\otimes} x {\otimes} f\left(i\right) {\otimes} z\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: 15 operands: 5
4	Operation	operator: 9 operand: 8
5	ExprTuple	18, 19, 20, 21, 7, 23
6	ExprTuple	8
7	Operation	operator: 9 operand: 12
8	Lambda	parameter: 29 body: 11
9	Literal
10	ExprTuple	12
11	Conditional	value: 13 condition: 17
12	Lambda	parameter: 29 body: 14
13	Operation	operator: 15 operands: 16
14	Conditional	value: 22 condition: 17
15	Literal
16	ExprTuple	18, 19, 20, 21, 22, 23
17	Operation	operator: 24 operands: 25
18	Variable
19	Variable
20	Variable
21	Variable
22	Operation	operator: 26 operand: 29
23	Variable
24	Literal
25	ExprTuple	29, 28
26	Variable
27	ExprTuple	29
28	Operation	operator: 30 operands: 31
29	Variable
30	Literal
31	ExprTuple	32, 33
32	Literal
33	Literal