Expression of type Lambda

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, 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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 19 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10
8	Operation	operator: 29 operand: 15
9	Operation	operator: 12 operands: 13
10	ExprRange	lambda_map: 14 start_index: 27 end_index: 28
11	ExprTuple	15
12	Literal
13	ExprTuple	16
14	Lambda	parameter: 35 body: 17
15	Operation	operator: 18 operands: 19
16	ExprRange	lambda_map: 20 start_index: 27 end_index: 28
17	Operation	operator: 21 operands: 22
18	Literal
19	ExprTuple	23
20	Lambda	parameter: 35 body: 24
21	Literal
22	ExprTuple	32, 25
23	ExprRange	lambda_map: 26 start_index: 27 end_index: 28
24	Operation	operator: 29 operand: 32
25	IndexedVar	variable: 31 index: 35
26	Lambda	parameter: 35 body: 32
27	Literal
28	Variable
29	Literal
30	ExprTuple	32
31	Variable
32	IndexedVar	variable: 33 index: 35
33	Variable
34	ExprTuple	35
35	Variable