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, ExprTuple, K, Lambda, i
from proveit.core_expr_types import V_1_to_i
from proveit.linear_algebra import TensorProd, VecSpaces
from proveit.logic import Forall, InClass, InSet
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
sub_expr1 = VecSpaces(K)
expr = ExprTuple(Lambda(i, Conditional(Forall(instance_param_or_params = [V_1_to_i], instance_expr = InClass(TensorProd(V_1_to_i), sub_expr1), domain = sub_expr1), InSet(i, NaturalPos))))

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(i \mapsto \left\{\forall_{V_{1}, V_{2}, \ldots, V_{i} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left(\left(V_{1} {\otimes}  V_{2} {\otimes}  \ldots {\otimes}  V_{i}\right) \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) \textrm{ if } i \in \mathbb{N}^+\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	parameter: 27 body: 3
2	ExprTuple	27
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	27, 11
10	Lambda	parameters: 21 body: 12
11	Literal
12	Conditional	value: 13 condition: 14
13	Operation	operator: 28 operands: 15
14	Operation	operator: 16 operands: 17
15	ExprTuple	18, 31
16	Literal
17	ExprTuple	19
18	Operation	operator: 20 operands: 21
19	ExprRange	lambda_map: 22 start_index: 26 end_index: 27
20	Literal
21	ExprTuple	23
22	Lambda	parameter: 36 body: 24
23	ExprRange	lambda_map: 25 start_index: 26 end_index: 27
24	Operation	operator: 28 operands: 29
25	Lambda	parameter: 36 body: 30
26	Literal
27	Variable
28	Literal
29	ExprTuple	30, 31
30	IndexedVar	variable: 32 index: 36
31	Operation	operator: 34 operand: 37
32	Variable
33	ExprTuple	36
34	Literal
35	ExprTuple	37
36	Variable
37	Variable