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, i, x, y
from proveit.linear_algebra import TensorProd, VecSum
from proveit.logic import CartExp, Equals, Forall, InSet
from proveit.numbers import Interval, Real, four, three, two

# build up the expression from sub-expressions
sub_expr1 = [i]
sub_expr2 = TensorProd(x, y)
sub_expr3 = CartExp(Real, three)
sub_expr4 = Interval(two, four)
expr = ExprTuple(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(sub_expr2, TensorProd(sub_expr3, sub_expr3)), domain = sub_expr4), Equals(TensorProd(x, VecSum(index_or_indices = sub_expr1, summand = y, domain = sub_expr4)), VecSum(index_or_indices = sub_expr1, summand = sub_expr2, domain = sub_expr4)).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(\forall_{i \in \{2~\ldotp \ldotp~4\}}~\left(\left(x {\otimes} y\right) \in \left(\mathbb{R}^{3} {\otimes} \mathbb{R}^{3}\right)\right), \begin{array}{c} \begin{array}{l} \left(x {\otimes} \left(\sum_{i=2}^{4} y\right)\right) \\  = \left(\sum_{i=2}^{4} \left(x {\otimes} y\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: 3 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	8, 9
7	Lambda	parameter: 38 body: 10
8	Operation	operator: 26 operands: 11
9	Operation	operator: 17 operand: 15
10	Conditional	value: 13 condition: 29
11	ExprTuple	30, 14
12	ExprTuple	15
13	Operation	operator: 34 operands: 16
14	Operation	operator: 17 operand: 21
15	Lambda	parameter: 38 body: 19
16	ExprTuple	22, 20
17	Literal
18	ExprTuple	21
19	Conditional	value: 22 condition: 29
20	Operation	operator: 26 operands: 23
21	Lambda	parameter: 38 body: 25
22	Operation	operator: 26 operands: 27
23	ExprTuple	28, 28
24	ExprTuple	38
25	Conditional	value: 31 condition: 29
26	Literal
27	ExprTuple	30, 31
28	Operation	operator: 32 operands: 33
29	Operation	operator: 34 operands: 35
30	Variable
31	Variable
32	Literal
33	ExprTuple	36, 37
34	Literal
35	ExprTuple	38, 39
36	Literal
37	Literal
38	Variable
39	Operation	operator: 40 operands: 41
40	Literal
41	ExprTuple	42, 43
42	Literal
43	Literal