Expression of type Lambda

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, 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 = 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())

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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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