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, V, Variable, a, i
from proveit.core_expr_types import a_1_to_i
from proveit.linear_algebra import Norm, TensorProd
from proveit.logic import And, Equals, 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 = Conditional(Equals(Norm(TensorProd(a_1_to_i)), one), And(ExprRange(sub_expr1, InSet(sub_expr2, IndexedVar(V, sub_expr1)), one, i), And(ExprRange(sub_expr1, Equals(Norm(sub_expr2), one), one, i))))

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\{\left \|a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i}\right \| = 1 \textrm{ if } \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)\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: 26 operands: 3
2	Operation	operator: 10 operands: 4
3	ExprTuple	5, 29
4	ExprTuple	6, 7
5	Operation	operator: 30 operand: 12
6	ExprRange	lambda_map: 9 start_index: 29 end_index: 24
7	Operation	operator: 10 operands: 11
8	ExprTuple	12
9	Lambda	parameter: 35 body: 13
10	Literal
11	ExprTuple	14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operands: 18
14	ExprRange	lambda_map: 19 start_index: 29 end_index: 24
15	Literal
16	ExprTuple	20
17	Literal
18	ExprTuple	32, 21
19	Lambda	parameter: 35 body: 22
20	ExprRange	lambda_map: 23 start_index: 29 end_index: 24
21	IndexedVar	variable: 25 index: 35
22	Operation	operator: 26 operands: 27
23	Lambda	parameter: 35 body: 32
24	Variable
25	Variable
26	Literal
27	ExprTuple	28, 29
28	Operation	operator: 30 operand: 32
29	Literal
30	Literal
31	ExprTuple	32
32	IndexedVar	variable: 33 index: 35
33	Variable
34	ExprTuple	35
35	Variable