Expression of type InSet

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

# build up the expression from sub-expressions
sub_expr1 = CartExp(Real, three)
expr = InSet(VecSum(index_or_indices = [i], summand = TensorProd(y, fi), domain = Interval(two, four)), TensorProd(sub_expr1, sub_expr1))

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(\sum_{i=2}^{4} \left(y {\otimes} f\left(i\right)\right)\right) \in \left(\mathbb{R}^{3} {\otimes} \mathbb{R}^{3}\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 18 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 4 operand: 7
3	Operation	operator: 16 operands: 6
4	Literal
5	ExprTuple	7
6	ExprTuple	8, 8
7	Lambda	parameter: 27 body: 9
8	Operation	operator: 10 operands: 11
9	Conditional	value: 12 condition: 13
10	Literal
11	ExprTuple	14, 15
12	Operation	operator: 16 operands: 17
13	Operation	operator: 18 operands: 19
14	Literal
15	Literal
16	Literal
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	27, 22
20	Variable
21	Operation	operator: 23 operand: 27
22	Operation	operator: 25 operands: 26
23	Variable
24	ExprTuple	27
25	Literal
26	ExprTuple	28, 29
27	Variable
28	Literal
29	Literal