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

# build up the expression from sub-expressions
sub_expr1 = [i]
sub_expr2 = Interval(two, four)
expr = Equals(VecSum(index_or_indices = sub_expr1, summand = ScalarMult(gamma, ScalarMult(beta, TensorProd(x, fi, y))), domain = sub_expr2), ScalarMult(Mult(gamma, beta), TensorProd(x, VecSum(index_or_indices = sub_expr1, summand = fi, domain = sub_expr2), 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(\sum_{i=2}^{4} \left(\gamma \cdot \left(\beta \cdot \left(x {\otimes} f\left(i\right) {\otimes} y\right)\right)\right)\right) = \left(\left(\gamma \cdot \beta\right) \cdot \left(x {\otimes} \left(\sum_{i=2}^{4} f\left(i\right)\right) {\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: 17 operand: 7
4	Operation	operator: 22 operands: 6
5	ExprTuple	7
6	ExprTuple	8, 9
7	Lambda	parameter: 40 body: 10
8	Operation	operator: 11 operands: 12
9	Operation	operator: 28 operands: 13
10	Conditional	value: 14 condition: 27
11	Literal
12	ExprTuple	19, 25
13	ExprTuple	32, 15, 34
14	Operation	operator: 22 operands: 16
15	Operation	operator: 17 operand: 21
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21
19	Variable
20	Operation	operator: 22 operands: 23
21	Lambda	parameter: 40 body: 24
22	Literal
23	ExprTuple	25, 26
24	Conditional	value: 33 condition: 27
25	Variable
26	Operation	operator: 28 operands: 29
27	Operation	operator: 30 operands: 31
28	Literal
29	ExprTuple	32, 33, 34
30	Literal
31	ExprTuple	40, 35
32	Variable
33	Operation	operator: 36 operand: 40
34	Variable
35	Operation	operator: 38 operands: 39
36	Variable
37	ExprTuple	40
38	Literal
39	ExprTuple	41, 42
40	Variable
41	Literal
42	Literal