Expression of type ExprTuple

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 ExprTuple, beta, fi, gamma, i, x, y
from proveit.linear_algebra import ScalarMult, TensorProd, VecSum
from proveit.logic import CartExp, Equals, InSet
from proveit.numbers import Interval, Real, four, three, two

# build up the expression from sub-expressions
sub_expr1 = [i]
sub_expr2 = Interval(two, four)
sub_expr3 = CartExp(Real, three)
sub_expr4 = ScalarMult(gamma, beta)
sub_expr5 = TensorProd(x, fi, y)
sub_expr6 = VecSum(index_or_indices = sub_expr1, summand = sub_expr5, domain = sub_expr2)
expr = ExprTuple(InSet(sub_expr6, TensorProd(sub_expr3, sub_expr3, sub_expr3)), Equals(ScalarMult(sub_expr4, sub_expr6), VecSum(index_or_indices = sub_expr1, summand = ScalarMult(sub_expr4, sub_expr5), domain = sub_expr2)).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())

\left(\left(\sum_{i=2}^{4} \left(x {\otimes} f\left(i\right) {\otimes} y\right)\right) \in \left(\mathbb{R}^{3} {\otimes} \mathbb{R}^{3} {\otimes} \mathbb{R}^{3}\right), \begin{array}{c} \begin{array}{l} \left(\left(\gamma \cdot \beta\right) \cdot \left(\sum_{i=2}^{4} \left(x {\otimes} f\left(i\right) {\otimes} y\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) \end{array} \end{array}\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 29 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	13, 6
4	Literal
5	ExprTuple	7, 8
6	Operation	operator: 33 operands: 9
7	Operation	operator: 31 operands: 10
8	Operation	operator: 17 operand: 14
9	ExprTuple	12, 12, 12
10	ExprTuple	27, 13
11	ExprTuple	14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operand: 22
14	Lambda	parameter: 47 body: 19
15	Literal
16	ExprTuple	20, 21
17	Literal
18	ExprTuple	22
19	Conditional	value: 23 condition: 26
20	Literal
21	Literal
22	Lambda	parameter: 47 body: 24
23	Operation	operator: 31 operands: 25
24	Conditional	value: 28 condition: 26
25	ExprTuple	27, 28
26	Operation	operator: 29 operands: 30
27	Operation	operator: 31 operands: 32
28	Operation	operator: 33 operands: 34
29	Literal
30	ExprTuple	47, 35
31	Literal
32	ExprTuple	36, 37
33	Literal
34	ExprTuple	38, 39, 40
35	Operation	operator: 41 operands: 42
36	Variable
37	Variable
38	Variable
39	Operation	operator: 43 operand: 47
40	Variable
41	Literal
42	ExprTuple	45, 46
43	Variable
44	ExprTuple	47
45	Literal
46	Literal
47	Variable