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 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)), one), domains = sub_expr2, condition = And(ExprRange(sub_expr1, Equals(Norm(IndexedVar(a, sub_expr1)), one), one, i))).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}\right \| = 1\right) \land  \left(\left \|a_{2}\right \| = 1\right) \land  \ldots \land  \left(\left \|a_{i}\right \| = 1\right)}~\\
\left(\left \|a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i}\right \| = 1\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: 49 end_index: 44
4	Operation	operator: 7 operand: 10
5	Operation	operator: 27 operands: 9
6	Lambda	parameter: 55 body: 41
7	Literal
8	ExprTuple	10
9	ExprTuple	11
10	Lambda	parameters: 36 body: 12
11	ExprRange	lambda_map: 13 start_index: 49 end_index: 44
12	Conditional	value: 14 condition: 15
13	Lambda	parameter: 55 body: 16
14	Operation	operator: 46 operands: 17
15	Operation	operator: 27 operands: 18
16	Operation	operator: 19 operands: 20
17	ExprTuple	21, 49
18	ExprTuple	22, 23
19	Literal
20	ExprTuple	41, 24
21	Operation	operator: 50 operand: 31
22	ExprRange	lambda_map: 26 start_index: 49 end_index: 44
23	Operation	operator: 27 operands: 28
24	Operation	operator: 29 operand: 34
25	ExprTuple	31
26	Lambda	parameter: 55 body: 32
27	Literal
28	ExprTuple	33
29	Literal
30	ExprTuple	34
31	Operation	operator: 35 operands: 36
32	Operation	operator: 37 operands: 38
33	ExprRange	lambda_map: 39 start_index: 49 end_index: 44
34	Variable
35	Literal
36	ExprTuple	40
37	Literal
38	ExprTuple	52, 41
39	Lambda	parameter: 55 body: 42
40	ExprRange	lambda_map: 43 start_index: 49 end_index: 44
41	IndexedVar	variable: 45 index: 55
42	Operation	operator: 46 operands: 47
43	Lambda	parameter: 55 body: 52
44	Variable
45	Variable
46	Literal
47	ExprTuple	48, 49
48	Operation	operator: 50 operand: 52
49	Literal
50	Literal
51	ExprTuple	52
52	IndexedVar	variable: 53 index: 55
53	Variable
54	ExprTuple	55
55	Variable