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, a_1_to_i
from proveit.linear_algebra import TensorProd, VecSpaces
from proveit.logic import Forall, InSet
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
sub_expr1 = [V_1_to_i]
expr = ExprTuple(Lambda(i, Conditional(Forall(instance_param_or_params = sub_expr1, instance_expr = Forall(instance_param_or_params = [a_1_to_i], instance_expr = InSet(TensorProd(a_1_to_i), TensorProd(V_1_to_i)), domains = sub_expr1), domain = VecSpaces(K)), 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[\forall_{\left(a_{1} \in V_{1}\right), \left(a_{2} \in V_{2}\right), \ldots, \left(a_{i} \in V_{i}\right)}~\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)\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: 45 body: 3
2	ExprTuple	45
3	Conditional	value: 4 condition: 5
4	Operation	operator: 13 operand: 8
5	Operation	operator: 46 operands: 7
6	ExprTuple	8
7	ExprTuple	45, 9
8	Lambda	parameters: 34 body: 10
9	Literal
10	Conditional	value: 11 condition: 12
11	Operation	operator: 13 operand: 16
12	Operation	operator: 24 operands: 15
13	Literal
14	ExprTuple	16
15	ExprTuple	17
16	Lambda	parameters: 32 body: 18
17	ExprRange	lambda_map: 19 start_index: 44 end_index: 45
18	Conditional	value: 20 condition: 21
19	Lambda	parameter: 53 body: 22
20	Operation	operator: 46 operands: 23
21	Operation	operator: 24 operands: 25
22	Operation	operator: 26 operands: 27
23	ExprTuple	28, 29
24	Literal
25	ExprTuple	30
26	Literal
27	ExprTuple	49, 31
28	Operation	operator: 33 operands: 32
29	Operation	operator: 33 operands: 34
30	ExprRange	lambda_map: 35 start_index: 44 end_index: 45
31	Operation	operator: 36 operand: 41
32	ExprTuple	38
33	Literal
34	ExprTuple	39
35	Lambda	parameter: 53 body: 40
36	Literal
37	ExprTuple	41
38	ExprRange	lambda_map: 42 start_index: 44 end_index: 45
39	ExprRange	lambda_map: 43 start_index: 44 end_index: 45
40	Operation	operator: 46 operands: 47
41	Variable
42	Lambda	parameter: 53 body: 48
43	Lambda	parameter: 53 body: 49
44	Literal
45	Variable
46	Literal
47	ExprTuple	48, 49
48	IndexedVar	variable: 50 index: 53
49	IndexedVar	variable: 51 index: 53
50	Variable
51	Variable
52	ExprTuple	53
53	Variable