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 Conditional, 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 And, Equals, Forall, InSet
from proveit.numbers import 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(i, Conditional(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)), one), domains = sub_expr2, condition = And(ExprRange(sub_expr1, Equals(Norm(IndexedVar(a, sub_expr1)), one), one, i))).with_wrapping(), domain = InnerProdSpaces(K)).with_wrapping(), InSet(i, 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(i \mapsto \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}\right \| = 1\right) \land  \left(\left \|a_{2}\right \| = 1\right) \land  \ldots \land  \left(\left \|a_{i}\right \| = 1\right)}~\\
\left(\left \|a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i}\right \| = 1\right)\end{array}\right]\end{array} \textrm{ if } i \in \mathbb{N}^+\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: 53 body: 3
2	ExprTuple	53
3	Conditional	value: 4 condition: 5
4	Operation	operator: 16 operand: 8
5	Operation	operator: 46 operands: 7
6	ExprTuple	8
7	ExprTuple	53, 9
8	Lambda	parameters: 10 body: 11
9	Literal
10	ExprTuple	12
11	Conditional	value: 13 condition: 14
12	ExprRange	lambda_map: 15 start_index: 58 end_index: 53
13	Operation	operator: 16 operand: 19
14	Operation	operator: 36 operands: 18
15	Lambda	parameter: 64 body: 50
16	Literal
17	ExprTuple	19
18	ExprTuple	20
19	Lambda	parameters: 45 body: 21
20	ExprRange	lambda_map: 22 start_index: 58 end_index: 53
21	Conditional	value: 23 condition: 24
22	Lambda	parameter: 64 body: 25
23	Operation	operator: 55 operands: 26
24	Operation	operator: 36 operands: 27
25	Operation	operator: 28 operands: 29
26	ExprTuple	30, 58
27	ExprTuple	31, 32
28	Literal
29	ExprTuple	50, 33
30	Operation	operator: 59 operand: 40
31	ExprRange	lambda_map: 35 start_index: 58 end_index: 53
32	Operation	operator: 36 operands: 37
33	Operation	operator: 38 operand: 43
34	ExprTuple	40
35	Lambda	parameter: 64 body: 41
36	Literal
37	ExprTuple	42
38	Literal
39	ExprTuple	43
40	Operation	operator: 44 operands: 45
41	Operation	operator: 46 operands: 47
42	ExprRange	lambda_map: 48 start_index: 58 end_index: 53
43	Variable
44	Literal
45	ExprTuple	49
46	Literal
47	ExprTuple	61, 50
48	Lambda	parameter: 64 body: 51
49	ExprRange	lambda_map: 52 start_index: 58 end_index: 53
50	IndexedVar	variable: 54 index: 64
51	Operation	operator: 55 operands: 56
52	Lambda	parameter: 64 body: 61
53	Variable
54	Variable
55	Literal
56	ExprTuple	57, 58
57	Operation	operator: 59 operand: 61
58	Literal
59	Literal
60	ExprTuple	61
61	IndexedVar	variable: 62 index: 64
62	Variable
63	ExprTuple	64
64	Variable