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