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 Conditional, ExprTuple, Lambda, 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 = ExprTuple(Lambda(i, 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(i \mapsto \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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 11 body: 3
2	ExprTuple	11
3	Conditional	value: 4 condition: 5
4	Operation	operator: 7 operands: 6
5	Operation	operator: 7 operands: 8
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12
9	Operation	operator: 14 operands: 13
10	Operation	operator: 14 operands: 15
11	Variable
12	Operation	operator: 16 operands: 17
13	ExprTuple	18, 19
14	Literal
15	ExprTuple	20, 20
16	Literal
17	ExprTuple	21, 22
18	Operation	operator: 24 operands: 23
19	Operation	operator: 24 operands: 25
20	Operation	operator: 26 operands: 27
21	Literal
22	Literal
23	ExprTuple	29, 28
24	Literal
25	ExprTuple	29, 30
26	Literal
27	ExprTuple	31, 32
28	Variable
29	Variable
30	Variable
31	Literal
32	Literal