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, 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 = ExprTuple(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(\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..\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: 2 body: 3
2	ExprTuple	4
3	Conditional	value: 5 condition: 6
4	ExprRange	lambda_map: 7 start_index: 50 end_index: 45
5	Operation	operator: 8 operand: 11
6	Operation	operator: 28 operands: 10
7	Lambda	parameter: 56 body: 42
8	Literal
9	ExprTuple	11
10	ExprTuple	12
11	Lambda	parameters: 37 body: 13
12	ExprRange	lambda_map: 14 start_index: 50 end_index: 45
13	Conditional	value: 15 condition: 16
14	Lambda	parameter: 56 body: 17
15	Operation	operator: 47 operands: 18
16	Operation	operator: 28 operands: 19
17	Operation	operator: 20 operands: 21
18	ExprTuple	22, 50
19	ExprTuple	23, 24
20	Literal
21	ExprTuple	42, 25
22	Operation	operator: 51 operand: 32
23	ExprRange	lambda_map: 27 start_index: 50 end_index: 45
24	Operation	operator: 28 operands: 29
25	Operation	operator: 30 operand: 35
26	ExprTuple	32
27	Lambda	parameter: 56 body: 33
28	Literal
29	ExprTuple	34
30	Literal
31	ExprTuple	35
32	Operation	operator: 36 operands: 37
33	Operation	operator: 38 operands: 39
34	ExprRange	lambda_map: 40 start_index: 50 end_index: 45
35	Variable
36	Literal
37	ExprTuple	41
38	Literal
39	ExprTuple	53, 42
40	Lambda	parameter: 56 body: 43
41	ExprRange	lambda_map: 44 start_index: 50 end_index: 45
42	IndexedVar	variable: 46 index: 56
43	Operation	operator: 47 operands: 48
44	Lambda	parameter: 56 body: 53
45	Variable
46	Variable
47	Literal
48	ExprTuple	49, 50
49	Operation	operator: 51 operand: 53
50	Literal
51	Literal
52	ExprTuple	53
53	IndexedVar	variable: 54 index: 56
54	Variable
55	ExprTuple	56
56	Variable