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 Conditional, 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(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())

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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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