Expression of type Conditional

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, 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 = 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())

\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()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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