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 Mult, 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)), Mult(ExprRange(sub_expr1, Norm(sub_expr2), one, i))), And(ExprRange(sub_expr1, InSet(sub_expr2, IndexedVar(V, sub_expr1)), 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 \| = \left(\left \|a_{1}\right \| \cdot  \left \|a_{2}\right \| \cdot  \ldots \cdot  \left \|a_{i}\right \|\right) \textrm{ if } \left(a_{1} \in V_{1}\right) \land  \left(a_{2} \in V_{2}\right) \land  \ldots \land  \left(a_{i} \in V_{i}\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: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9
7	Operation	operator: 28 operand: 14
8	Operation	operator: 11 operands: 12
9	ExprRange	lambda_map: 13 start_index: 26 end_index: 27
10	ExprTuple	14
11	Literal
12	ExprTuple	15
13	Lambda	parameter: 34 body: 16
14	Operation	operator: 17 operands: 18
15	ExprRange	lambda_map: 19 start_index: 26 end_index: 27
16	Operation	operator: 20 operands: 21
17	Literal
18	ExprTuple	22
19	Lambda	parameter: 34 body: 23
20	Literal
21	ExprTuple	31, 24
22	ExprRange	lambda_map: 25 start_index: 26 end_index: 27
23	Operation	operator: 28 operand: 31
24	IndexedVar	variable: 30 index: 34
25	Lambda	parameter: 34 body: 31
26	Literal
27	Variable
28	Literal
29	ExprTuple	31
30	Variable
31	IndexedVar	variable: 32 index: 34
32	Variable
33	ExprTuple	34
34	Variable