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

# build up the expression from sub-expressions
sub_expr1 = VecSpaces(K)
expr = ExprTuple(Lambda(K, Forall(instance_param_or_params = [i], instance_expr = Forall(instance_param_or_params = [V_1_to_i], instance_expr = InClass(TensorProd(V_1_to_i), sub_expr1), domain = sub_expr1), 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(\left(V_{1} {\otimes}  V_{2} {\otimes}  \ldots {\otimes}  V_{i}\right) \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\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: 40 body: 2
2	Operation	operator: 9 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 30 body: 6
5	ExprTuple	30
6	Conditional	value: 7 condition: 8
7	Operation	operator: 9 operand: 13
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	13
11	Literal
12	ExprTuple	30, 14
13	Lambda	parameters: 24 body: 15
14	Literal
15	Conditional	value: 16 condition: 17
16	Operation	operator: 31 operands: 18
17	Operation	operator: 19 operands: 20
18	ExprTuple	21, 34
19	Literal
20	ExprTuple	22
21	Operation	operator: 23 operands: 24
22	ExprRange	lambda_map: 25 start_index: 29 end_index: 30
23	Literal
24	ExprTuple	26
25	Lambda	parameter: 39 body: 27
26	ExprRange	lambda_map: 28 start_index: 29 end_index: 30
27	Operation	operator: 31 operands: 32
28	Lambda	parameter: 39 body: 33
29	Literal
30	Variable
31	Literal
32	ExprTuple	33, 34
33	IndexedVar	variable: 35 index: 39
34	Operation	operator: 37 operand: 40
35	Variable
36	ExprTuple	39
37	Literal
38	ExprTuple	40
39	Variable
40	Variable