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, W, n, v
from proveit.core_expr_types import A_1_to_n, V_1_to_n, v_1_to_n
from proveit.linear_algebra import LinMap, TensorProd
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(A, sub_expr1)
expr = ExprTuple(Lambda([A_1_to_n], Conditional(Forall(instance_param_or_params = [v_1_to_n], instance_expr = Equals(Function(TensorProd(A_1_to_n), [TensorProd(v_1_to_n)]), TensorProd(ExprRange(sub_expr1, Function(sub_expr2, [IndexedVar(v, sub_expr1)]), one, n))), domains = [V_1_to_n]).with_wrapping(), And(ExprRange(sub_expr1, InSet(sub_expr2, LinMap(IndexedVar(V, sub_expr1), IndexedVar(W, 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}, A_{2}, \ldots, A_{n}\right) \mapsto \left\{\begin{array}{l}\forall_{\left(v_{1} \in V_{1}\right), \left(v_{2} \in V_{2}\right), \ldots, \left(v_{n} \in V_{n}\right)}~\\
\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)\right)\end{array} \textrm{ if } \left(A_{1} \in \mathcal{L}\left(V_{1}, W_{1}\right)\right) \land  \left(A_{2} \in \mathcal{L}\left(V_{2}, W_{2}\right)\right) \land  \ldots \land  \left(A_{n} \in \mathcal{L}\left(V_{n}, W_{n}\right)\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: 30 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 17 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9
8	Lambda	parameters: 37 body: 10
9	ExprRange	lambda_map: 11 start_index: 47 end_index: 48
10	Conditional	value: 12 condition: 13
11	Lambda	parameter: 56 body: 14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operands: 18
14	Operation	operator: 39 operands: 19
15	Literal
16	ExprTuple	20, 21
17	Literal
18	ExprTuple	22
19	ExprTuple	49, 23
20	Operation	operator: 24 operand: 31
21	Operation	operator: 36 operands: 26
22	ExprRange	lambda_map: 27 start_index: 47 end_index: 48
23	Operation	operator: 28 operands: 29
24	Operation	operator: 36 operands: 30
25	ExprTuple	31
26	ExprTuple	32
27	Lambda	parameter: 56 body: 33
28	Literal
29	ExprTuple	45, 34
30	ExprTuple	35
31	Operation	operator: 36 operands: 37
32	ExprRange	lambda_map: 38 start_index: 47 end_index: 48
33	Operation	operator: 39 operands: 40
34	IndexedVar	variable: 41 index: 56
35	ExprRange	lambda_map: 42 start_index: 47 end_index: 48
36	Literal
37	ExprTuple	43
38	Lambda	parameter: 56 body: 44
39	Literal
40	ExprTuple	53, 45
41	Variable
42	Lambda	parameter: 56 body: 49
43	ExprRange	lambda_map: 46 start_index: 47 end_index: 48
44	Operation	operator: 49 operand: 53
45	IndexedVar	variable: 51 index: 56
46	Lambda	parameter: 56 body: 53
47	Literal
48	Variable
49	IndexedVar	variable: 52 index: 56
50	ExprTuple	53
51	Variable
52	Variable
53	IndexedVar	variable: 54 index: 56
54	Variable
55	ExprTuple	56
56	Variable