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, ExprRange, IndexedVar, K, V, Variable, 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 And, Forall, InClass, InSet
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Forall(instance_param_or_params = [a_1_to_i], instance_expr = InSet(TensorProd(a_1_to_i), TensorProd(V_1_to_i)), domains = [V_1_to_i]), And(ExprRange(sub_expr1, InClass(IndexedVar(V, sub_expr1), VecSpaces(K)), one, i)))

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_{\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) \textrm{ if } \left(V_{1} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) \land  \left(V_{2} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) \land  \ldots \land  \left(V_{i} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right)\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: 3 operand: 6
2	Operation	operator: 14 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7
6	Lambda	parameters: 22 body: 8
7	ExprRange	lambda_map: 9 start_index: 34 end_index: 35
8	Conditional	value: 10 condition: 11
9	Lambda	parameter: 43 body: 12
10	Operation	operator: 36 operands: 13
11	Operation	operator: 14 operands: 15
12	Operation	operator: 16 operands: 17
13	ExprTuple	18, 19
14	Literal
15	ExprTuple	20
16	Literal
17	ExprTuple	39, 21
18	Operation	operator: 23 operands: 22
19	Operation	operator: 23 operands: 24
20	ExprRange	lambda_map: 25 start_index: 34 end_index: 35
21	Operation	operator: 26 operand: 31
22	ExprTuple	28
23	Literal
24	ExprTuple	29
25	Lambda	parameter: 43 body: 30
26	Literal
27	ExprTuple	31
28	ExprRange	lambda_map: 32 start_index: 34 end_index: 35
29	ExprRange	lambda_map: 33 start_index: 34 end_index: 35
30	Operation	operator: 36 operands: 37
31	Variable
32	Lambda	parameter: 43 body: 38
33	Lambda	parameter: 43 body: 39
34	Literal
35	Variable
36	Literal
37	ExprTuple	38, 39
38	IndexedVar	variable: 40 index: 43
39	IndexedVar	variable: 41 index: 43
40	Variable
41	Variable
42	ExprTuple	43
43	Variable