Expression of type Lambda

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 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 = 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())

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]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 39 body: 1
1	Operation	operator: 8 operand: 3
2	ExprTuple	3
3	Lambda	parameter: 29 body: 5
4	ExprTuple	29
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operand: 12
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12
10	Literal
11	ExprTuple	29, 13
12	Lambda	parameters: 23 body: 14
13	Literal
14	Conditional	value: 15 condition: 16
15	Operation	operator: 30 operands: 17
16	Operation	operator: 18 operands: 19
17	ExprTuple	20, 33
18	Literal
19	ExprTuple	21
20	Operation	operator: 22 operands: 23
21	ExprRange	lambda_map: 24 start_index: 28 end_index: 29
22	Literal
23	ExprTuple	25
24	Lambda	parameter: 38 body: 26
25	ExprRange	lambda_map: 27 start_index: 28 end_index: 29
26	Operation	operator: 30 operands: 31
27	Lambda	parameter: 38 body: 32
28	Literal
29	Variable
30	Literal
31	ExprTuple	32, 33
32	IndexedVar	variable: 34 index: 38
33	Operation	operator: 36 operand: 39
34	Variable
35	ExprTuple	38
36	Literal
37	ExprTuple	39
38	Variable
39	Variable