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, ExprRange, ExprTuple, IndexedVar, K, Lambda, V, Variable, i
from proveit.core_expr_types import V_1_to_i
from proveit.linear_algebra import TensorProd, VecSpaces
from proveit.logic import And, InClass
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = VecSpaces(K)
expr = ExprTuple(Lambda([V_1_to_i], Conditional(InClass(TensorProd(V_1_to_i), sub_expr2), And(ExprRange(sub_expr1, InClass(IndexedVar(V, sub_expr1), sub_expr2), 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(V_{1}, V_{2}, \ldots, V_{i}\right) \mapsto \left\{\left(V_{1} {\otimes}  V_{2} {\otimes}  \ldots {\otimes}  V_{i}\right) \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right) \textrm{ if } \left(V_{1} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) \land  \left(V_{2} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) \land  \ldots \land  \left(V_{i} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right)\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	parameters: 11 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 18 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 21
6	Literal
7	ExprTuple	9
8	Operation	operator: 10 operands: 11
9	ExprRange	lambda_map: 12 start_index: 16 end_index: 17
10	Literal
11	ExprTuple	13
12	Lambda	parameter: 26 body: 14
13	ExprRange	lambda_map: 15 start_index: 16 end_index: 17
14	Operation	operator: 18 operands: 19
15	Lambda	parameter: 26 body: 20
16	Literal
17	Variable
18	Literal
19	ExprTuple	20, 21
20	IndexedVar	variable: 22 index: 26
21	Operation	operator: 24 operand: 27
22	Variable
23	ExprTuple	26
24	Literal
25	ExprTuple	27
26	Variable
27	Variable