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 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(K, Forall(instance_param_or_params = [i], instance_expr = 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)), domain = 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(K \mapsto \left[\forall_{i \in \mathbb{N}^+}~\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]\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	parameter: 44 body: 2
2	Operation	operator: 16 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 48 body: 6
5	ExprTuple	48
6	Conditional	value: 7 condition: 8
7	Operation	operator: 16 operand: 11
8	Operation	operator: 49 operands: 10
9	ExprTuple	11
10	ExprTuple	48, 12
11	Lambda	parameters: 37 body: 13
12	Literal
13	Conditional	value: 14 condition: 15
14	Operation	operator: 16 operand: 19
15	Operation	operator: 27 operands: 18
16	Literal
17	ExprTuple	19
18	ExprTuple	20
19	Lambda	parameters: 35 body: 21
20	ExprRange	lambda_map: 22 start_index: 47 end_index: 48
21	Conditional	value: 23 condition: 24
22	Lambda	parameter: 56 body: 25
23	Operation	operator: 49 operands: 26
24	Operation	operator: 27 operands: 28
25	Operation	operator: 29 operands: 30
26	ExprTuple	31, 32
27	Literal
28	ExprTuple	33
29	Literal
30	ExprTuple	52, 34
31	Operation	operator: 36 operands: 35
32	Operation	operator: 36 operands: 37
33	ExprRange	lambda_map: 38 start_index: 47 end_index: 48
34	Operation	operator: 39 operand: 44
35	ExprTuple	41
36	Literal
37	ExprTuple	42
38	Lambda	parameter: 56 body: 43
39	Literal
40	ExprTuple	44
41	ExprRange	lambda_map: 45 start_index: 47 end_index: 48
42	ExprRange	lambda_map: 46 start_index: 47 end_index: 48
43	Operation	operator: 49 operands: 50
44	Variable
45	Lambda	parameter: 56 body: 51
46	Lambda	parameter: 56 body: 52
47	Literal
48	Variable
49	Literal
50	ExprTuple	51, 52
51	IndexedVar	variable: 53 index: 56
52	IndexedVar	variable: 54 index: 56
53	Variable
54	Variable
55	ExprTuple	56
56	Variable