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, ExprRange, IndexedVar, 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 = 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\{\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()

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: 20 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8
6	Operation	operator: 10 operands: 9
7	Operation	operator: 10 operands: 11
8	ExprRange	lambda_map: 12 start_index: 18 end_index: 19
9	ExprTuple	13
10	Literal
11	ExprTuple	14
12	Lambda	parameter: 27 body: 15
13	ExprRange	lambda_map: 16 start_index: 18 end_index: 19
14	ExprRange	lambda_map: 17 start_index: 18 end_index: 19
15	Operation	operator: 20 operands: 21
16	Lambda	parameter: 27 body: 22
17	Lambda	parameter: 27 body: 23
18	Literal
19	Variable
20	Literal
21	ExprTuple	22, 23
22	IndexedVar	variable: 24 index: 27
23	IndexedVar	variable: 25 index: 27
24	Variable
25	Variable
26	ExprTuple	27
27	Variable