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 = VecSum(index_or_indices = [i], summand = y, domain = Interval(two, four))
expr = Equals(ScalarMult(beta, TensorProd(x, ScalarMult(beta, sub_expr1))), ScalarMult(beta, ScalarMult(beta, TensorProd(x, 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(\beta \cdot \left(x {\otimes} \left(\beta \cdot \left(\sum_{i=2}^{4} y\right)\right)\right)\right) = \left(\beta \cdot \left(\beta \cdot \left(x {\otimes} \left(\sum_{i=2}^{4} y\right)\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: 13 operands: 5
4	Operation	operator: 13 operands: 6
5	ExprTuple	17, 7
6	ExprTuple	17, 8
7	Operation	operator: 15 operands: 9
8	Operation	operator: 13 operands: 10
9	ExprTuple	18, 11
10	ExprTuple	17, 12
11	Operation	operator: 13 operands: 14
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	17, 19
15	Literal
16	ExprTuple	18, 19
17	Variable
18	Variable
19	Operation	operator: 20 operand: 22
20	Literal
21	ExprTuple	22
22	Lambda	parameter: 29 body: 24
23	ExprTuple	29
24	Conditional	value: 25 condition: 26
25	Variable
26	Operation	operator: 27 operands: 28
27	Literal
28	ExprTuple	29, 30
29	Variable
30	Operation	operator: 31 operands: 32
31	Literal
32	ExprTuple	33, 34
33	Literal
34	Literal