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

# build up the expression from sub-expressions
sub_expr1 = [i]
sub_expr2 = CartExp(Real, three)
sub_expr3 = Interval(two, four)
sub_expr4 = TensorProd(x, y, fi, z)
sub_expr5 = TensorProd(sub_expr2, sub_expr2, sub_expr2, sub_expr2)
expr = ExprTuple(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(sub_expr4, sub_expr5), domain = sub_expr3), InSet(VecSum(index_or_indices = sub_expr1, summand = sub_expr4, domain = sub_expr3), sub_expr5))

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 {\otimes} f\left(i\right) {\otimes} z\right) \in \left(\mathbb{R}^{3} {\otimes} \mathbb{R}^{3} {\otimes} \mathbb{R}^{3} {\otimes} \mathbb{R}^{3}\right)\right), \left(\sum_{i=2}^{4} \left(x {\otimes} y {\otimes} f\left(i\right) {\otimes} z\right)\right) \in \left(\mathbb{R}^{3} {\otimes} \mathbb{R}^{3} {\otimes} \mathbb{R}^{3} {\otimes} \mathbb{R}^{3}\right)\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: 6
2	Operation	operator: 21 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 15
6	Lambda	parameter: 37 body: 8
7	Operation	operator: 9 operand: 12
8	Conditional	value: 11 condition: 17
9	Literal
10	ExprTuple	12
11	Operation	operator: 21 operands: 13
12	Lambda	parameter: 37 body: 14
13	ExprTuple	16, 15
14	Conditional	value: 16 condition: 17
15	Operation	operator: 19 operands: 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	ExprTuple	23, 23, 23, 23
19	Literal
20	ExprTuple	24, 25, 26, 27
21	Literal
22	ExprTuple	37, 28
23	Operation	operator: 29 operands: 30
24	Variable
25	Variable
26	Operation	operator: 31 operand: 37
27	Variable
28	Operation	operator: 33 operands: 34
29	Literal
30	ExprTuple	35, 36
31	Variable
32	ExprTuple	37
33	Literal
34	ExprTuple	38, 39
35	Literal
36	Literal
37	Variable
38	Literal
39	Literal