Expression of type Conditional

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 Conditional, beta, i, x, y
from proveit.linear_algebra import ScalarMult, TensorProd
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 = Conditional(InSet(TensorProd(ScalarMult(beta, x), ScalarMult(beta, y)), TensorProd(sub_expr1, sub_expr1)), InSet(i, Interval(two, four)))

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(\left(\beta \cdot x\right) {\otimes} \left(\beta \cdot y\right)\right) \in \left(\mathbb{R}^{3} {\otimes} \mathbb{R}^{3}\right) \textrm{ if } i \in \{2~\ldotp \ldotp~4\}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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