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, ExprRange, IndexedVar, Lambda, V, Variable, a, i
from proveit.core_expr_types import V_1_to_i, a_1_to_i
from proveit.linear_algebra import TensorProd
from proveit.logic import And, InSet
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda([a_1_to_i], Conditional(InSet(TensorProd(a_1_to_i), TensorProd(V_1_to_i)), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), IndexedVar(V, sub_expr1)), one, i))))

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(a_{1}, a_{2}, \ldots, a_{i}\right) \mapsto \left\{\left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i}\right) \in \left(V_{1} {\otimes}  V_{2} {\otimes}  \ldots {\otimes}  V_{i}\right) \textrm{ if } \left(a_{1} \in V_{1}\right) \land  \left(a_{2} \in V_{2}\right) \land  \ldots \land  \left(a_{i} \in V_{i}\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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