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 ExprRange, ExprTuple, IndexedVar, K, Lambda, Variable, a, i
from proveit.core_expr_types import V_1_to_i, a_1_to_i
from proveit.linear_algebra import InnerProdSpaces, Norm, TensorProd
from proveit.logic import Equals, Forall
from proveit.numbers import Mult, NaturalPos, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = [V_1_to_i]
expr = ExprTuple(Lambda(K, Forall(instance_param_or_params = [i], instance_expr = Forall(instance_param_or_params = sub_expr2, instance_expr = Forall(instance_param_or_params = [a_1_to_i], instance_expr = Equals(Norm(TensorProd(a_1_to_i)), Mult(ExprRange(sub_expr1, Norm(IndexedVar(a, sub_expr1)), one, i))), domains = sub_expr2).with_wrapping(), domain = InnerProdSpaces(K)).with_wrapping(), domain = NaturalPos)))

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(K \mapsto \left[\forall_{i \in \mathbb{N}^+}~\left[\begin{array}{l}\forall_{V_{1}, V_{2}, \ldots, V_{i} \underset{{\scriptscriptstyle c}}{\in} \textrm{InnerProdSpaces}\left(K\right)}~\\
\left[\begin{array}{l}\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 \| = \left(\left \|a_{1}\right \| \cdot  \left \|a_{2}\right \| \cdot  \ldots \cdot  \left \|a_{i}\right \|\right)\right)\end{array}\right]\end{array}\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	parameter: 48 body: 2
2	Operation	operator: 19 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 59 body: 6
5	ExprTuple	59
6	Conditional	value: 7 condition: 8
7	Operation	operator: 19 operand: 11
8	Operation	operator: 52 operands: 10
9	ExprTuple	11
10	ExprTuple	59, 12
11	Lambda	parameters: 13 body: 14
12	Literal
13	ExprTuple	15
14	Conditional	value: 16 condition: 17
15	ExprRange	lambda_map: 18 start_index: 58 end_index: 59
16	Operation	operator: 19 operand: 22
17	Operation	operator: 31 operands: 21
18	Lambda	parameter: 66 body: 56
19	Literal
20	ExprTuple	22
21	ExprTuple	23
22	Lambda	parameters: 50 body: 24
23	ExprRange	lambda_map: 25 start_index: 58 end_index: 59
24	Conditional	value: 26 condition: 27
25	Lambda	parameter: 66 body: 28
26	Operation	operator: 29 operands: 30
27	Operation	operator: 31 operands: 32
28	Operation	operator: 33 operands: 34
29	Literal
30	ExprTuple	35, 36
31	Literal
32	ExprTuple	37
33	Literal
34	ExprTuple	56, 38
35	Operation	operator: 60 operand: 45
36	Operation	operator: 40 operands: 41
37	ExprRange	lambda_map: 42 start_index: 58 end_index: 59
38	Operation	operator: 43 operand: 48
39	ExprTuple	45
40	Literal
41	ExprTuple	46
42	Lambda	parameter: 66 body: 47
43	Literal
44	ExprTuple	48
45	Operation	operator: 49 operands: 50
46	ExprRange	lambda_map: 51 start_index: 58 end_index: 59
47	Operation	operator: 52 operands: 53
48	Variable
49	Literal
50	ExprTuple	54
51	Lambda	parameter: 66 body: 55
52	Literal
53	ExprTuple	63, 56
54	ExprRange	lambda_map: 57 start_index: 58 end_index: 59
55	Operation	operator: 60 operand: 63
56	IndexedVar	variable: 62 index: 66
57	Lambda	parameter: 66 body: 63
58	Literal
59	Variable
60	Literal
61	ExprTuple	63
62	Variable
63	IndexedVar	variable: 64 index: 66
64	Variable
65	ExprTuple	66
66	Variable