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, 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 = 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())

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]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 43 body: 1
1	Operation	operator: 15 operand: 3
2	ExprTuple	3
3	Lambda	parameter: 47 body: 5
4	ExprTuple	47
5	Conditional	value: 6 condition: 7
6	Operation	operator: 15 operand: 10
7	Operation	operator: 48 operands: 9
8	ExprTuple	10
9	ExprTuple	47, 11
10	Lambda	parameters: 36 body: 12
11	Literal
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operand: 18
14	Operation	operator: 26 operands: 17
15	Literal
16	ExprTuple	18
17	ExprTuple	19
18	Lambda	parameters: 34 body: 20
19	ExprRange	lambda_map: 21 start_index: 46 end_index: 47
20	Conditional	value: 22 condition: 23
21	Lambda	parameter: 55 body: 24
22	Operation	operator: 48 operands: 25
23	Operation	operator: 26 operands: 27
24	Operation	operator: 28 operands: 29
25	ExprTuple	30, 31
26	Literal
27	ExprTuple	32
28	Literal
29	ExprTuple	51, 33
30	Operation	operator: 35 operands: 34
31	Operation	operator: 35 operands: 36
32	ExprRange	lambda_map: 37 start_index: 46 end_index: 47
33	Operation	operator: 38 operand: 43
34	ExprTuple	40
35	Literal
36	ExprTuple	41
37	Lambda	parameter: 55 body: 42
38	Literal
39	ExprTuple	43
40	ExprRange	lambda_map: 44 start_index: 46 end_index: 47
41	ExprRange	lambda_map: 45 start_index: 46 end_index: 47
42	Operation	operator: 48 operands: 49
43	Variable
44	Lambda	parameter: 55 body: 50
45	Lambda	parameter: 55 body: 51
46	Literal
47	Variable
48	Literal
49	ExprTuple	50, 51
50	IndexedVar	variable: 52 index: 55
51	IndexedVar	variable: 53 index: 55
52	Variable
53	Variable
54	ExprTuple	55
55	Variable