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 fi, gamma, i, x, y, z
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)
expr = Equals(TensorProd(x, VecSum(index_or_indices = sub_expr1, summand = ScalarMult(gamma, TensorProd(y, fi)), domain = sub_expr2), z), TensorProd(x, ScalarMult(gamma, TensorProd(y, VecSum(index_or_indices = sub_expr1, summand = fi, domain = sub_expr2))), z))

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