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 = ScalarMult(gamma, beta)
sub_expr3 = Interval(two, four)
expr = Equals(TensorProd(x, VecSum(index_or_indices = sub_expr1, summand = ScalarMult(sub_expr2, fi), domain = sub_expr3), y), VecSum(index_or_indices = sub_expr1, summand = ScalarMult(sub_expr2, TensorProd(x, fi, y)), domain = sub_expr3)).with_wrapping_at(1)

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())

\begin{array}{c} \begin{array}{l} \left(x {\otimes} \left(\sum_{i=2}^{4} \left(\left(\gamma \cdot \beta\right) \cdot f\left(i\right)\right)\right) {\otimes} y\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) \end{array} \end{array}

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.	()	(1)	('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: 22 operands: 5
4	Operation	operator: 9 operand: 8
5	ExprTuple	26, 7, 28
6	ExprTuple	8
7	Operation	operator: 9 operand: 12
8	Lambda	parameter: 39 body: 11
9	Literal
10	ExprTuple	12
11	Conditional	value: 13 condition: 17
12	Lambda	parameter: 39 body: 14
13	Operation	operator: 29 operands: 15
14	Conditional	value: 16 condition: 17
15	ExprTuple	24, 18
16	Operation	operator: 29 operands: 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	ExprTuple	24, 27
20	Literal
21	ExprTuple	39, 25
22	Literal
23	ExprTuple	26, 27, 28
24	Operation	operator: 29 operands: 30
25	Operation	operator: 31 operands: 32
26	Variable
27	Operation	operator: 33 operand: 39
28	Variable
29	Literal
30	ExprTuple	35, 36
31	Literal
32	ExprTuple	37, 38
33	Variable
34	ExprTuple	39
35	Variable
36	Variable
37	Literal
38	Literal
39	Variable