Expression of type Lambda

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, 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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 29 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operand: 7
3	Operation	operator: 16 operands: 6
4	Literal
5	ExprTuple	7
6	ExprTuple	8
7	Lambda	parameters: 36 body: 9
8	ExprRange	lambda_map: 10 start_index: 46 end_index: 47
9	Conditional	value: 11 condition: 12
10	Lambda	parameter: 55 body: 13
11	Operation	operator: 14 operands: 15
12	Operation	operator: 16 operands: 17
13	Operation	operator: 38 operands: 18
14	Literal
15	ExprTuple	19, 20
16	Literal
17	ExprTuple	21
18	ExprTuple	48, 22
19	Operation	operator: 23 operand: 30
20	Operation	operator: 35 operands: 25
21	ExprRange	lambda_map: 26 start_index: 46 end_index: 47
22	Operation	operator: 27 operands: 28
23	Operation	operator: 35 operands: 29
24	ExprTuple	30
25	ExprTuple	31
26	Lambda	parameter: 55 body: 32
27	Literal
28	ExprTuple	44, 33
29	ExprTuple	34
30	Operation	operator: 35 operands: 36
31	ExprRange	lambda_map: 37 start_index: 46 end_index: 47
32	Operation	operator: 38 operands: 39
33	IndexedVar	variable: 40 index: 55
34	ExprRange	lambda_map: 41 start_index: 46 end_index: 47
35	Literal
36	ExprTuple	42
37	Lambda	parameter: 55 body: 43
38	Literal
39	ExprTuple	52, 44
40	Variable
41	Lambda	parameter: 55 body: 48
42	ExprRange	lambda_map: 45 start_index: 46 end_index: 47
43	Operation	operator: 48 operand: 52
44	IndexedVar	variable: 50 index: 55
45	Lambda	parameter: 55 body: 52
46	Literal
47	Variable
48	IndexedVar	variable: 51 index: 55
49	ExprTuple	52
50	Variable
51	Variable
52	IndexedVar	variable: 53 index: 55
53	Variable
54	ExprTuple	55
55	Variable