Expression of type Conditional

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, IndexedVar, K, 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 = 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\{\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..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 13 operand: 5
2	Operation	operator: 43 operands: 4
3	ExprTuple	5
4	ExprTuple	50, 6
5	Lambda	parameters: 7 body: 8
6	Literal
7	ExprTuple	9
8	Conditional	value: 10 condition: 11
9	ExprRange	lambda_map: 12 start_index: 55 end_index: 50
10	Operation	operator: 13 operand: 16
11	Operation	operator: 33 operands: 15
12	Lambda	parameter: 61 body: 47
13	Literal
14	ExprTuple	16
15	ExprTuple	17
16	Lambda	parameters: 42 body: 18
17	ExprRange	lambda_map: 19 start_index: 55 end_index: 50
18	Conditional	value: 20 condition: 21
19	Lambda	parameter: 61 body: 22
20	Operation	operator: 52 operands: 23
21	Operation	operator: 33 operands: 24
22	Operation	operator: 25 operands: 26
23	ExprTuple	27, 55
24	ExprTuple	28, 29
25	Literal
26	ExprTuple	47, 30
27	Operation	operator: 56 operand: 37
28	ExprRange	lambda_map: 32 start_index: 55 end_index: 50
29	Operation	operator: 33 operands: 34
30	Operation	operator: 35 operand: 40
31	ExprTuple	37
32	Lambda	parameter: 61 body: 38
33	Literal
34	ExprTuple	39
35	Literal
36	ExprTuple	40
37	Operation	operator: 41 operands: 42
38	Operation	operator: 43 operands: 44
39	ExprRange	lambda_map: 45 start_index: 55 end_index: 50
40	Variable
41	Literal
42	ExprTuple	46
43	Literal
44	ExprTuple	58, 47
45	Lambda	parameter: 61 body: 48
46	ExprRange	lambda_map: 49 start_index: 55 end_index: 50
47	IndexedVar	variable: 51 index: 61
48	Operation	operator: 52 operands: 53
49	Lambda	parameter: 61 body: 58
50	Variable
51	Variable
52	Literal
53	ExprTuple	54, 55
54	Operation	operator: 56 operand: 58
55	Literal
56	Literal
57	ExprTuple	58
58	IndexedVar	variable: 59 index: 61
59	Variable
60	ExprTuple	61
61	Variable