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 And, Equals, Forall
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(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)), 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(), 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}\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}\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: 46 body: 2
2	Operation	operator: 19 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 56 body: 6
5	ExprTuple	56
6	Conditional	value: 7 condition: 8
7	Operation	operator: 19 operand: 11
8	Operation	operator: 49 operands: 10
9	ExprTuple	11
10	ExprTuple	56, 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: 61 end_index: 56
16	Operation	operator: 19 operand: 22
17	Operation	operator: 39 operands: 21
18	Lambda	parameter: 67 body: 53
19	Literal
20	ExprTuple	22
21	ExprTuple	23
22	Lambda	parameters: 48 body: 24
23	ExprRange	lambda_map: 25 start_index: 61 end_index: 56
24	Conditional	value: 26 condition: 27
25	Lambda	parameter: 67 body: 28
26	Operation	operator: 58 operands: 29
27	Operation	operator: 39 operands: 30
28	Operation	operator: 31 operands: 32
29	ExprTuple	33, 61
30	ExprTuple	34, 35
31	Literal
32	ExprTuple	53, 36
33	Operation	operator: 62 operand: 43
34	ExprRange	lambda_map: 38 start_index: 61 end_index: 56
35	Operation	operator: 39 operands: 40
36	Operation	operator: 41 operand: 46
37	ExprTuple	43
38	Lambda	parameter: 67 body: 44
39	Literal
40	ExprTuple	45
41	Literal
42	ExprTuple	46
43	Operation	operator: 47 operands: 48
44	Operation	operator: 49 operands: 50
45	ExprRange	lambda_map: 51 start_index: 61 end_index: 56
46	Variable
47	Literal
48	ExprTuple	52
49	Literal
50	ExprTuple	64, 53
51	Lambda	parameter: 67 body: 54
52	ExprRange	lambda_map: 55 start_index: 61 end_index: 56
53	IndexedVar	variable: 57 index: 67
54	Operation	operator: 58 operands: 59
55	Lambda	parameter: 67 body: 64
56	Variable
57	Variable
58	Literal
59	ExprTuple	60, 61
60	Operation	operator: 62 operand: 64
61	Literal
62	Literal
63	ExprTuple	64
64	IndexedVar	variable: 65 index: 67
65	Variable
66	ExprTuple	67
67	Variable