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, Lambda, 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 = ExprTuple(Lambda([a_1_to_i], 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}, a_{2}, \ldots, a_{i}\right) \mapsto \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..\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	parameters: 20 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11
9	Operation	operator: 30 operand: 16
10	Operation	operator: 13 operands: 14
11	ExprRange	lambda_map: 15 start_index: 28 end_index: 29
12	ExprTuple	16
13	Literal
14	ExprTuple	17
15	Lambda	parameter: 36 body: 18
16	Operation	operator: 19 operands: 20
17	ExprRange	lambda_map: 21 start_index: 28 end_index: 29
18	Operation	operator: 22 operands: 23
19	Literal
20	ExprTuple	24
21	Lambda	parameter: 36 body: 25
22	Literal
23	ExprTuple	33, 26
24	ExprRange	lambda_map: 27 start_index: 28 end_index: 29
25	Operation	operator: 30 operand: 33
26	IndexedVar	variable: 32 index: 36
27	Lambda	parameter: 36 body: 33
28	Literal
29	Variable
30	Literal
31	ExprTuple	33
32	Variable
33	IndexedVar	variable: 34 index: 36
34	Variable
35	ExprTuple	36
36	Variable