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, K, Lambda, V, Variable, a, i
from proveit.core_expr_types import V_1_to_i, a_1_to_i
from proveit.linear_algebra import InnerProdSpaces, Norm, TensorProd
from proveit.logic import And, Equals, Forall, InClass
from proveit.numbers import Mult, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = [V_1_to_i]
expr = Lambda(sub_expr2, Conditional(Forall(instance_param_or_params = [a_1_to_i], instance_expr = Equals(Norm(TensorProd(a_1_to_i)), Mult(ExprRange(sub_expr1, Norm(IndexedVar(a, sub_expr1)), one, i))), domains = sub_expr2).with_wrapping(), And(ExprRange(sub_expr1, InClass(IndexedVar(V, sub_expr1), InnerProdSpaces(K)), 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(V_{1}, V_{2}, \ldots, V_{i}\right) \mapsto \left\{\begin{array}{l}\forall_{\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} {\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)\right)\end{array} \textrm{ if } \left(V_{1} \underset{{\scriptscriptstyle c}}{\in} \textrm{InnerProdSpaces}\left(K\right)\right) \land  \left(V_{2} \underset{{\scriptscriptstyle c}}{\in} \textrm{InnerProdSpaces}\left(K\right)\right) \land  \ldots \land  \left(V_{i} \underset{{\scriptscriptstyle c}}{\in} \textrm{InnerProdSpaces}\left(K\right)\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: 1 body: 2
1	ExprTuple	3
2	Conditional	value: 4 condition: 5
3	ExprRange	lambda_map: 6 start_index: 46 end_index: 47
4	Operation	operator: 7 operand: 10
5	Operation	operator: 19 operands: 9
6	Lambda	parameter: 54 body: 44
7	Literal
8	ExprTuple	10
9	ExprTuple	11
10	Lambda	parameters: 38 body: 12
11	ExprRange	lambda_map: 13 start_index: 46 end_index: 47
12	Conditional	value: 14 condition: 15
13	Lambda	parameter: 54 body: 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	Operation	operator: 21 operands: 22
17	Literal
18	ExprTuple	23, 24
19	Literal
20	ExprTuple	25
21	Literal
22	ExprTuple	44, 26
23	Operation	operator: 48 operand: 33
24	Operation	operator: 28 operands: 29
25	ExprRange	lambda_map: 30 start_index: 46 end_index: 47
26	Operation	operator: 31 operand: 36
27	ExprTuple	33
28	Literal
29	ExprTuple	34
30	Lambda	parameter: 54 body: 35
31	Literal
32	ExprTuple	36
33	Operation	operator: 37 operands: 38
34	ExprRange	lambda_map: 39 start_index: 46 end_index: 47
35	Operation	operator: 40 operands: 41
36	Variable
37	Literal
38	ExprTuple	42
39	Lambda	parameter: 54 body: 43
40	Literal
41	ExprTuple	51, 44
42	ExprRange	lambda_map: 45 start_index: 46 end_index: 47
43	Operation	operator: 48 operand: 51
44	IndexedVar	variable: 50 index: 54
45	Lambda	parameter: 54 body: 51
46	Literal
47	Variable
48	Literal
49	ExprTuple	51
50	Variable
51	IndexedVar	variable: 52 index: 54
52	Variable
53	ExprTuple	54
54	Variable