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, fi, i, x, z
from proveit.linear_algebra import TensorProd, VecSum
from proveit.logic import CartExp, Equals, Forall, InSet
from proveit.numbers import Interval, Real, one, three

# build up the expression from sub-expressions
sub_expr1 = [i]
sub_expr2 = CartExp(Real, three)
sub_expr3 = Interval(one, three)
sub_expr4 = TensorProd(x, fi, z)
expr = ExprTuple(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(sub_expr4, TensorProd(sub_expr2, sub_expr2, sub_expr2)), domain = sub_expr3), Equals(TensorProd(x, VecSum(index_or_indices = sub_expr1, summand = fi, domain = sub_expr3), z), VecSum(index_or_indices = sub_expr1, summand = sub_expr4, 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(\forall_{i \in \{1~\ldotp \ldotp~3\}}~\left(\left(x {\otimes} f\left(i\right) {\otimes} z\right) \in \left(\mathbb{R}^{3} {\otimes} \mathbb{R}^{3} {\otimes} \mathbb{R}^{3}\right)\right), \begin{array}{c} \begin{array}{l} \left(x {\otimes} \left(\sum_{i=1}^{3} f\left(i\right)\right) {\otimes} z\right) \\  = \left(\sum_{i=1}^{3} \left(x {\otimes} f\left(i\right) {\otimes} z\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: 40 body: 10
8	Operation	operator: 25 operands: 11
9	Operation	operator: 17 operand: 15
10	Conditional	value: 13 condition: 28
11	ExprTuple	29, 14, 31
12	ExprTuple	15
13	Operation	operator: 34 operands: 16
14	Operation	operator: 17 operand: 21
15	Lambda	parameter: 40 body: 19
16	ExprTuple	22, 20
17	Literal
18	ExprTuple	21
19	Conditional	value: 22 condition: 28
20	Operation	operator: 25 operands: 23
21	Lambda	parameter: 40 body: 24
22	Operation	operator: 25 operands: 26
23	ExprTuple	27, 27, 27
24	Conditional	value: 30 condition: 28
25	Literal
26	ExprTuple	29, 30, 31
27	Operation	operator: 32 operands: 33
28	Operation	operator: 34 operands: 35
29	Variable
30	Operation	operator: 36 operand: 40
31	Variable
32	Literal
33	ExprTuple	38, 44
34	Literal
35	ExprTuple	40, 39
36	Variable
37	ExprTuple	40
38	Literal
39	Operation	operator: 41 operands: 42
40	Variable
41	Literal
42	ExprTuple	43, 44
43	Literal
44	Literal