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 beta, i, x, y
from proveit.linear_algebra import ScalarMult, TensorProd, VecSum
from proveit.logic import Equals
from proveit.numbers import Interval, four, two

# build up the expression from sub-expressions
sub_expr1 = [i]
sub_expr2 = Interval(two, four)
sub_expr3 = ScalarMult(beta, y)
expr = Equals(TensorProd(VecSum(index_or_indices = sub_expr1, summand = ScalarMult(beta, x), domain = sub_expr2), sub_expr3), TensorProd(ScalarMult(beta, VecSum(index_or_indices = sub_expr1, summand = x, domain = sub_expr2)), sub_expr3))

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(\sum_{i=2}^{4} \left(\beta \cdot x\right)\right) {\otimes} \left(\beta \cdot y\right)\right) = \left(\left(\beta \cdot \left(\sum_{i=2}^{4} x\right)\right) {\otimes} \left(\beta \cdot y\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, 10
6	Literal
7	ExprTuple	9, 10
8	Operation	operator: 18 operand: 14
9	Operation	operator: 22 operands: 12
10	Operation	operator: 22 operands: 13
11	ExprTuple	14
12	ExprTuple	26, 15
13	ExprTuple	26, 16
14	Lambda	parameter: 31 body: 17
15	Operation	operator: 18 operand: 21
16	Variable
17	Conditional	value: 20 condition: 28
18	Literal
19	ExprTuple	21
20	Operation	operator: 22 operands: 23
21	Lambda	parameter: 31 body: 25
22	Literal
23	ExprTuple	26, 27
24	ExprTuple	31
25	Conditional	value: 27 condition: 28
26	Variable
27	Variable
28	Operation	operator: 29 operands: 30
29	Literal
30	ExprTuple	31, 32
31	Variable
32	Operation	operator: 33 operands: 34
33	Literal
34	ExprTuple	35, 36
35	Literal
36	Literal