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 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)), 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}, a_{2}, \ldots, a_{i}\right) \mapsto \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..\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: 18 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 28 operands: 5
4	Operation	operator: 12 operands: 6
5	ExprTuple	7, 31
6	ExprTuple	8, 9
7	Operation	operator: 32 operand: 14
8	ExprRange	lambda_map: 11 start_index: 31 end_index: 26
9	Operation	operator: 12 operands: 13
10	ExprTuple	14
11	Lambda	parameter: 37 body: 15
12	Literal
13	ExprTuple	16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	ExprRange	lambda_map: 21 start_index: 31 end_index: 26
17	Literal
18	ExprTuple	22
19	Literal
20	ExprTuple	34, 23
21	Lambda	parameter: 37 body: 24
22	ExprRange	lambda_map: 25 start_index: 31 end_index: 26
23	IndexedVar	variable: 27 index: 37
24	Operation	operator: 28 operands: 29
25	Lambda	parameter: 37 body: 34
26	Variable
27	Variable
28	Literal
29	ExprTuple	30, 31
30	Operation	operator: 32 operand: 34
31	Literal
32	Literal
33	ExprTuple	34
34	IndexedVar	variable: 35 index: 37
35	Variable
36	ExprTuple	37
37	Variable