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, x, y
from proveit.linear_algebra import ScalarMult, TensorProd
from proveit.logic import Equals
from proveit.numbers import Add, Exp, Mult, four, one, subtract, three, two

# build up the expression from sub-expressions
expr = Equals(ScalarMult(Add(subtract(four, two), one), TensorProd(ScalarMult(beta, x), ScalarMult(beta, y))), ScalarMult(Mult(three, Exp(beta, two)), TensorProd(x, y)))

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(\left(4 - 2\right) + 1\right) \cdot \left(\left(\beta \cdot x\right) {\otimes} \left(\beta \cdot y\right)\right)\right) = \left(\left(3 \cdot \beta^{2}\right) \cdot \left(x {\otimes} 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: 26 operands: 5
4	Operation	operator: 26 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	9, 10
7	Operation	operator: 23 operands: 11
8	Operation	operator: 15 operands: 12
9	Operation	operator: 13 operands: 14
10	Operation	operator: 15 operands: 16
11	ExprTuple	17, 18
12	ExprTuple	19, 20
13	Literal
14	ExprTuple	21, 22
15	Literal
16	ExprTuple	32, 33
17	Operation	operator: 23 operands: 24
18	Literal
19	Operation	operator: 26 operands: 25
20	Operation	operator: 26 operands: 27
21	Literal
22	Operation	operator: 28 operands: 29
23	Literal
24	ExprTuple	30, 31
25	ExprTuple	34, 32
26	Literal
27	ExprTuple	34, 33
28	Literal
29	ExprTuple	34, 37
30	Literal
31	Operation	operator: 35 operand: 37
32	Variable
33	Variable
34	Variable
35	Literal
36	ExprTuple	37
37	Literal