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, fi, i, x, z
from proveit.linear_algebra import 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(x, fi, z), TensorProd(sub_expr1, 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(x {\otimes} f\left(i\right) {\otimes} z\right) \in \left(\mathbb{R}^{3} {\otimes} \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: 25 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 5 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	25, 9
7	Operation	operator: 11 operands: 10
8	Operation	operator: 11 operands: 12
9	Operation	operator: 13 operands: 14
10	ExprTuple	15, 16, 17
11	Literal
12	ExprTuple	18, 18, 18
13	Literal
14	ExprTuple	19, 20
15	Variable
16	Operation	operator: 21 operand: 25
17	Variable
18	Operation	operator: 23 operands: 24
19	Literal
20	Literal
21	Variable
22	ExprTuple	25
23	Literal
24	ExprTuple	26, 27
25	Variable
26	Literal
27	Literal