Expression of type Conditional ¶

from the theory of proveit.linear_algebra.inner_products ¶

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, H, n, v, w
from proveit.core_expr_types import x_1_to_n
from proveit.linear_algebra import Bases, InnerProd, OrthoNormBases
from proveit.logic import And, Equals, Forall, InSet, Set
from proveit.numbers import KroneckerDelta, NaturalPos

# build up the expression from sub-expressions
sub_expr1 = Set(x_1_to_n)
expr = Conditional(Forall(instance_param_or_params = [x_1_to_n], instance_expr = Equals(InSet(sub_expr1, OrthoNormBases(H)), And(InSet(sub_expr1, Bases(H)), Forall(instance_param_or_params = [v, w], instance_expr = Equals(InnerProd(v, w), KroneckerDelta(v, w)), domain = sub_expr1))).with_wrapping_at(2), domain = H), InSet(n, 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\{\forall_{x_{1}, x_{2}, \ldots, x_{n} \in H}~\left(\begin{array}{c} \begin{array}{l} \left(\left\{x_{1}, x_{2}, \ldots, x_{n}\right\} \in \textrm{O.N.Bases}\left(H\right)\right) =  \\ \left(\left(\left\{x_{1}, x_{2}, \ldots, x_{n}\right\} \in \textrm{Bases}\left(H\right)\right) \land \left[\forall_{v, w \in \left\{x_{1}, x_{2}, \ldots, x_{n}\right\}}~\left(\left \langle v, w\right \rangle = \delta_{v, w}\right)\right]\right) \end{array} \end{array}\right) \textrm{ if } n \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: 24 operand: 5
2	Operation	operator: 47 operands: 4
3	ExprTuple	5
4	ExprTuple	57, 6
5	Lambda	parameters: 53 body: 7
6	Literal
7	Conditional	value: 8 condition: 9
8	Operation	operator: 35 operands: 10
9	Operation	operator: 37 operands: 11
10	ExprTuple	12, 13
11	ExprTuple	14
12	Operation	operator: 47 operands: 15
13	Operation	operator: 37 operands: 16
14	ExprRange	lambda_map: 17 start_index: 56 end_index: 57
15	ExprTuple	51, 18
16	ExprTuple	19, 20
17	Lambda	parameter: 61 body: 21
18	Operation	operator: 22 operand: 32
19	Operation	operator: 47 operands: 23
20	Operation	operator: 24 operand: 28
21	Operation	operator: 47 operands: 26
22	Literal
23	ExprTuple	51, 27
24	Literal
25	ExprTuple	28
26	ExprTuple	58, 32
27	Operation	operator: 29 operand: 32
28	Lambda	parameters: 45 body: 31
29	Literal
30	ExprTuple	32
31	Conditional	value: 33 condition: 34
32	Variable
33	Operation	operator: 35 operands: 36
34	Operation	operator: 37 operands: 38
35	Literal
36	ExprTuple	39, 40
37	Literal
38	ExprTuple	41, 42
39	Operation	operator: 43 operands: 45
40	Operation	operator: 44 operands: 45
41	Operation	operator: 47 operands: 46
42	Operation	operator: 47 operands: 48
43	Literal
44	Literal
45	ExprTuple	49, 50
46	ExprTuple	49, 51
47	Literal
48	ExprTuple	50, 51
49	Variable
50	Variable
51	Operation	operator: 52 operands: 53
52	Literal
53	ExprTuple	54
54	ExprRange	lambda_map: 55 start_index: 56 end_index: 57
55	Lambda	parameter: 61 body: 58
56	Literal
57	Variable
58	IndexedVar	variable: 59 index: 61
59	Variable
60	ExprTuple	61
61	Variable

Expression of type Conditional¶

from the theory of proveit.linear_algebra.inner_products¶

Expression of type Conditional ¶

from the theory of proveit.linear_algebra.inner_products ¶