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, 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 Equals, Forall, InSet
from proveit.numbers import Mult, NaturalPos, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = [V_1_to_i]
expr = Conditional(Forall(instance_param_or_params = sub_expr2, instance_expr = 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(), domain = InnerProdSpaces(K)).with_wrapping(), InSet(i, NaturalPos))

# 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_{V_{1}, V_{2}, \ldots, V_{i} \underset{{\scriptscriptstyle c}}{\in} \textrm{InnerProdSpaces}\left(K\right)}~\\
\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}\right]\end{array} \textrm{ if } i \in \mathbb{N}^+\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Conditional	value: 1 condition: 2
1	Operation	operator: 13 operand: 5
2	Operation	operator: 46 operands: 4
3	ExprTuple	5
4	ExprTuple	53, 6
5	Lambda	parameters: 7 body: 8
6	Literal
7	ExprTuple	9
8	Conditional	value: 10 condition: 11
9	ExprRange	lambda_map: 12 start_index: 52 end_index: 53
10	Operation	operator: 13 operand: 16
11	Operation	operator: 25 operands: 15
12	Lambda	parameter: 60 body: 50
13	Literal
14	ExprTuple	16
15	ExprTuple	17
16	Lambda	parameters: 44 body: 18
17	ExprRange	lambda_map: 19 start_index: 52 end_index: 53
18	Conditional	value: 20 condition: 21
19	Lambda	parameter: 60 body: 22
20	Operation	operator: 23 operands: 24
21	Operation	operator: 25 operands: 26
22	Operation	operator: 27 operands: 28
23	Literal
24	ExprTuple	29, 30
25	Literal
26	ExprTuple	31
27	Literal
28	ExprTuple	50, 32
29	Operation	operator: 54 operand: 39
30	Operation	operator: 34 operands: 35
31	ExprRange	lambda_map: 36 start_index: 52 end_index: 53
32	Operation	operator: 37 operand: 42
33	ExprTuple	39
34	Literal
35	ExprTuple	40
36	Lambda	parameter: 60 body: 41
37	Literal
38	ExprTuple	42
39	Operation	operator: 43 operands: 44
40	ExprRange	lambda_map: 45 start_index: 52 end_index: 53
41	Operation	operator: 46 operands: 47
42	Variable
43	Literal
44	ExprTuple	48
45	Lambda	parameter: 60 body: 49
46	Literal
47	ExprTuple	57, 50
48	ExprRange	lambda_map: 51 start_index: 52 end_index: 53
49	Operation	operator: 54 operand: 57
50	IndexedVar	variable: 56 index: 60
51	Lambda	parameter: 60 body: 57
52	Literal
53	Variable
54	Literal
55	ExprTuple	57
56	Variable
57	IndexedVar	variable: 58 index: 60
58	Variable
59	ExprTuple	60
60	Variable

Expression of type Conditional¶

from the theory of proveit.linear_algebra.tensors¶

Expression of type Conditional ¶

from the theory of proveit.linear_algebra.tensors ¶