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 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)), 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 17 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 27 operands: 4
3	Operation	operator: 11 operands: 5
4	ExprTuple	6, 30
5	ExprTuple	7, 8
6	Operation	operator: 31 operand: 13
7	ExprRange	lambda_map: 10 start_index: 30 end_index: 25
8	Operation	operator: 11 operands: 12
9	ExprTuple	13
10	Lambda	parameter: 36 body: 14
11	Literal
12	ExprTuple	15
13	Operation	operator: 16 operands: 17
14	Operation	operator: 18 operands: 19
15	ExprRange	lambda_map: 20 start_index: 30 end_index: 25
16	Literal
17	ExprTuple	21
18	Literal
19	ExprTuple	33, 22
20	Lambda	parameter: 36 body: 23
21	ExprRange	lambda_map: 24 start_index: 30 end_index: 25
22	IndexedVar	variable: 26 index: 36
23	Operation	operator: 27 operands: 28
24	Lambda	parameter: 36 body: 33
25	Variable
26	Variable
27	Literal
28	ExprTuple	29, 30
29	Operation	operator: 31 operand: 33
30	Literal
31	Literal
32	ExprTuple	33
33	IndexedVar	variable: 34 index: 36
34	Variable
35	ExprTuple	36
36	Variable