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 A, Conditional, ExprRange, Function, IndexedVar, V, Variable, n, v
from proveit.core_expr_types import A_1_to_n, v_1_to_n
from proveit.linear_algebra import TensorProd
from proveit.logic import And, Equals, InSet
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(v, sub_expr1)
expr = Conditional(Equals(Function(TensorProd(A_1_to_n), [TensorProd(v_1_to_n)]), TensorProd(ExprRange(sub_expr1, Function(IndexedVar(A, sub_expr1), [sub_expr2]), one, n))), And(ExprRange(sub_expr1, InSet(sub_expr2, IndexedVar(V, sub_expr1)), one, n)))

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\{\left(A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{n}\right)\left(v_{1} {\otimes}  v_{2} {\otimes}  \ldots {\otimes}  v_{n}\right) = \left(A_{1}\left(v_{1}\right) {\otimes}  A_{2}\left(v_{2}\right) {\otimes}  \ldots {\otimes}  A_{n}\left(v_{n}\right)\right) \textrm{ if } \left(v_{1} \in V_{1}\right) \land  \left(v_{2} \in V_{2}\right) \land  \ldots \land  \left(v_{n} \in V_{n}\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 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9
7	Operation	operator: 10 operand: 15
8	Operation	operator: 19 operands: 12
9	ExprRange	lambda_map: 13 start_index: 29 end_index: 30
10	Operation	operator: 19 operands: 14
11	ExprTuple	15
12	ExprTuple	16
13	Lambda	parameter: 38 body: 17
14	ExprTuple	18
15	Operation	operator: 19 operands: 20
16	ExprRange	lambda_map: 21 start_index: 29 end_index: 30
17	Operation	operator: 22 operands: 23
18	ExprRange	lambda_map: 24 start_index: 29 end_index: 30
19	Literal
20	ExprTuple	25
21	Lambda	parameter: 38 body: 26
22	Literal
23	ExprTuple	35, 27
24	Lambda	parameter: 38 body: 31
25	ExprRange	lambda_map: 28 start_index: 29 end_index: 30
26	Operation	operator: 31 operand: 35
27	IndexedVar	variable: 33 index: 38
28	Lambda	parameter: 38 body: 35
29	Literal
30	Variable
31	IndexedVar	variable: 34 index: 38
32	ExprTuple	35
33	Variable
34	Variable
35	IndexedVar	variable: 36 index: 38
36	Variable
37	ExprTuple	38
38	Variable