Expression of type Lambda ¶

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, ExprRange, H, IndexedVar, Lambda, Variable, n, v, w, x
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, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Set(x_1_to_n)
expr = Lambda([x_1_to_n], Conditional(Equals(InSet(sub_expr2, OrthoNormBases(H)), And(InSet(sub_expr2, Bases(H)), Forall(instance_param_or_params = [v, w], instance_expr = Equals(InnerProd(v, w), KroneckerDelta(v, w)), domain = sub_expr2))).with_wrapping_at(2), And(ExprRange(sub_expr1, InSet(IndexedVar(x, sub_expr1), H), one, n))))

# 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(x_{1}, x_{2}, \ldots, x_{n}\right) \mapsto \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} \textrm{ if } \left(x_{1} \in H\right) \land  \left(x_{2} \in H\right) \land  \ldots \land  \left(x_{n} \in H\right)\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

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

Expression of type Lambda¶

from the theory of proveit.linear_algebra.inner_products¶

Expression of type Lambda ¶

from the theory of proveit.linear_algebra.inner_products ¶