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

# build up the expression from sub-expressions
sub_expr1 = [i]
sub_expr2 = Mult(gamma, beta)
sub_expr3 = Interval(two, four)
sub_expr4 = Mult(i, Add(i, one))
expr = Equals(ScalarMult(sub_expr2, VecSum(index_or_indices = sub_expr1, summand = ScalarMult(sub_expr4, TensorProd(x, y)), domain = sub_expr3)), ScalarMult(sub_expr2, TensorProd(x, VecSum(index_or_indices = sub_expr1, summand = ScalarMult(sub_expr4, y), domain = 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(\gamma \cdot \beta\right) \cdot \left(\sum_{i=2}^{4} \left(\left(i \cdot \left(i + 1\right)\right) \cdot \left(x {\otimes} y\right)\right)\right)\right) = \left(\left(\gamma \cdot \beta\right) \cdot \left(x {\otimes} \left(\sum_{i=2}^{4} \left(\left(i \cdot \left(i + 1\right)\right) \cdot 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: 30 operands: 5
4	Operation	operator: 30 operands: 6
5	ExprTuple	8, 7
6	ExprTuple	8, 9
7	Operation	operator: 18 operand: 13
8	Operation	operator: 38 operands: 11
9	Operation	operator: 28 operands: 12
10	ExprTuple	13
11	ExprTuple	14, 15
12	ExprTuple	34, 16
13	Lambda	parameter: 47 body: 17
14	Variable
15	Variable
16	Operation	operator: 18 operand: 21
17	Conditional	value: 20 condition: 27
18	Literal
19	ExprTuple	21
20	Operation	operator: 30 operands: 22
21	Lambda	parameter: 47 body: 24
22	ExprTuple	35, 25
23	ExprTuple	47
24	Conditional	value: 26 condition: 27
25	Operation	operator: 28 operands: 29
26	Operation	operator: 30 operands: 31
27	Operation	operator: 32 operands: 33
28	Literal
29	ExprTuple	34, 36
30	Literal
31	ExprTuple	35, 36
32	Literal
33	ExprTuple	47, 37
34	Variable
35	Operation	operator: 38 operands: 39
36	Variable
37	Operation	operator: 40 operands: 41
38	Literal
39	ExprTuple	47, 42
40	Literal
41	ExprTuple	43, 44
42	Operation	operator: 45 operands: 46
43	Literal
44	Literal
45	Literal
46	ExprTuple	47, 48
47	Variable
48	Literal