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, four, two

# build up the expression from sub-expressions
sub_expr1 = [i]
sub_expr2 = Interval(two, four)
sub_expr3 = TensorProd(x, fi, y)
expr = Equals(VecSum(index_or_indices = sub_expr1, summand = ScalarMult(gamma, ScalarMult(beta, sub_expr3)), domain = sub_expr2), VecSum(index_or_indices = sub_expr1, summand = ScalarMult(ScalarMult(gamma, beta), sub_expr3), 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(\sum_{i=2}^{4} \left(\gamma \cdot \left(\beta \cdot \left(x {\otimes} f\left(i\right) {\otimes} y\right)\right)\right)\right) = \left(\sum_{i=2}^{4} \left(\left(\gamma \cdot \beta\right) \cdot \left(x {\otimes} f\left(i\right) {\otimes} y\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: 6 operand: 8
4	Operation	operator: 6 operand: 9
5	ExprTuple	8
6	Literal
7	ExprTuple	9
8	Lambda	parameter: 39 body: 10
9	Lambda	parameter: 39 body: 11
10	Conditional	value: 12 condition: 14
11	Conditional	value: 13 condition: 14
12	Operation	operator: 23 operands: 15
13	Operation	operator: 23 operands: 16
14	Operation	operator: 17 operands: 18
15	ExprTuple	28, 19
16	ExprTuple	20, 27
17	Literal
18	ExprTuple	39, 21
19	Operation	operator: 23 operands: 22
20	Operation	operator: 23 operands: 24
21	Operation	operator: 25 operands: 26
22	ExprTuple	29, 27
23	Literal
24	ExprTuple	28, 29
25	Literal
26	ExprTuple	30, 31
27	Operation	operator: 32 operands: 33
28	Variable
29	Variable
30	Literal
31	Literal
32	Literal
33	ExprTuple	34, 35, 36
34	Variable
35	Operation	operator: 37 operand: 39
36	Variable
37	Variable
38	ExprTuple	39
39	Variable