Expression of type Conditional

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, 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}")
expr = 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 = [V_1_to_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\{\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()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operand: 6
2	Operation	operator: 15 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7
6	Lambda	parameters: 34 body: 8
7	ExprRange	lambda_map: 9 start_index: 42 end_index: 43
8	Conditional	value: 10 condition: 11
9	Lambda	parameter: 50 body: 12
10	Operation	operator: 13 operands: 14
11	Operation	operator: 15 operands: 16
12	Operation	operator: 17 operands: 18
13	Literal
14	ExprTuple	19, 20
15	Literal
16	ExprTuple	21
17	Literal
18	ExprTuple	40, 22
19	Operation	operator: 44 operand: 29
20	Operation	operator: 24 operands: 25
21	ExprRange	lambda_map: 26 start_index: 42 end_index: 43
22	Operation	operator: 27 operand: 32
23	ExprTuple	29
24	Literal
25	ExprTuple	30
26	Lambda	parameter: 50 body: 31
27	Literal
28	ExprTuple	32
29	Operation	operator: 33 operands: 34
30	ExprRange	lambda_map: 35 start_index: 42 end_index: 43
31	Operation	operator: 36 operands: 37
32	Variable
33	Literal
34	ExprTuple	38
35	Lambda	parameter: 50 body: 39
36	Literal
37	ExprTuple	47, 40
38	ExprRange	lambda_map: 41 start_index: 42 end_index: 43
39	Operation	operator: 44 operand: 47
40	IndexedVar	variable: 46 index: 50
41	Lambda	parameter: 50 body: 47
42	Literal
43	Variable
44	Literal
45	ExprTuple	47
46	Variable
47	IndexedVar	variable: 48 index: 50
48	Variable
49	ExprTuple	50
50	Variable