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

# build up the expression from sub-expressions
sub_expr1 = [i]
sub_expr2 = TensorProd(x, y)
sub_expr3 = Interval(two, four)
sub_expr4 = CartExp(Real, three)
sub_expr5 = Mult(gamma, beta)
sub_expr6 = Mult(i, Add(i, one))
sub_expr7 = VecSum(index_or_indices = sub_expr1, summand = ScalarMult(sub_expr6, sub_expr2), domain = sub_expr3)
expr = ExprTuple(InSet(sub_expr7, TensorProd(sub_expr4, sub_expr4)), Equals(ScalarMult(sub_expr5, sub_expr7), VecSum(index_or_indices = sub_expr1, summand = ScalarMult(Mult(sub_expr5, sub_expr6), sub_expr2), 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())

\left(\left(\sum_{i=2}^{4} \left(\left(i \cdot \left(i + 1\right)\right) \cdot \left(x {\otimes} y\right)\right)\right) \in \left(\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(\left(i \cdot \left(i + 1\right)\right) \cdot \left(x {\otimes} y\right)\right)\right)\right) \\  = \left(\sum_{i=2}^{4} \left(\left(\left(\gamma \cdot \beta\right) \cdot \left(i \cdot \left(i + 1\right)\right)\right) \cdot \left(x {\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: 32 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	13, 6
4	Literal
5	ExprTuple	7, 8
6	Operation	operator: 39 operands: 9
7	Operation	operator: 30 operands: 10
8	Operation	operator: 17 operand: 14
9	ExprTuple	12, 12
10	ExprTuple	37, 13
11	ExprTuple	14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operand: 22
14	Lambda	parameter: 55 body: 19
15	Literal
16	ExprTuple	20, 21
17	Literal
18	ExprTuple	22
19	Conditional	value: 23 condition: 28
20	Literal
21	Literal
22	Lambda	parameter: 55 body: 25
23	Operation	operator: 30 operands: 26
24	ExprTuple	55
25	Conditional	value: 27 condition: 28
26	ExprTuple	29, 35
27	Operation	operator: 30 operands: 31
28	Operation	operator: 32 operands: 33
29	Operation	operator: 44 operands: 34
30	Literal
31	ExprTuple	38, 35
32	Literal
33	ExprTuple	55, 36
34	ExprTuple	37, 38
35	Operation	operator: 39 operands: 40
36	Operation	operator: 41 operands: 42
37	Operation	operator: 44 operands: 43
38	Operation	operator: 44 operands: 45
39	Literal
40	ExprTuple	46, 47
41	Literal
42	ExprTuple	48, 49
43	ExprTuple	50, 51
44	Literal
45	ExprTuple	55, 52
46	Variable
47	Variable
48	Literal
49	Literal
50	Variable
51	Variable
52	Operation	operator: 53 operands: 54
53	Literal
54	ExprTuple	55, 56
55	Variable
56	Literal