Expression of type ExprTuple

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, ExprTuple, Function, IndexedVar, Lambda, 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 = ExprTuple(Lambda([v_1_to_n], 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(v_{1}, v_{2}, \ldots, v_{n}\right) \mapsto \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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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