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