Expression of type Lambda ¶

from the theory of proveit.statistics ¶

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 A, B, C, Conditional, Lambda, Omega, Q, Qx, X, f, fx, x
from proveit.logic import Disjoint, Equals, Forall, InClass, Injections, SubsetEq, Union
from proveit.numbers import Add
from proveit.statistics import ProbOfAll, SampleSpaces

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Lambda(Omega, Conditional(Forall(instance_param_or_params = [A, B, C, X, Q], instance_expr = Forall(instance_param_or_params = [f], instance_expr = Equals(ProbOfAll(instance_param_or_params = sub_expr1, instance_element = fx, domain = C, condition = Qx), Add(ProbOfAll(instance_param_or_params = sub_expr1, instance_element = fx, domain = A, condition = Qx), ProbOfAll(instance_param_or_params = sub_expr1, instance_element = fx, domain = B, condition = Qx))), domain = Injections(X, Omega)), conditions = [SubsetEq(C, X), Equals(C, Union(A, B)), Disjoint(A, B)]).with_wrapping(), InClass(Omega, SampleSpaces)))

# 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())

\Omega \mapsto \left\{\begin{array}{l}\forall_{A, B, C, X, Q~|~C \subseteq X, C = \left(A \cup B\right), \textrm{disjoint}\left(A, B\right)}~\\
\left[\forall_{f \in \left[X \xrightarrow[]{\text{1-to-1}} \Omega\right]}~\left(\left[\textrm{Prob}_{x \in C~|~Q\left(x\right)}~f\left(x\right)\right] = \left(\left[\textrm{Prob}_{x \in A~|~Q\left(x\right)}~f\left(x\right)\right] + \left[\textrm{Prob}_{x \in B~|~Q\left(x\right)}~f\left(x\right)\right]\right)\right)\right]\end{array} \textrm{ if } \Omega \underset{{\scriptscriptstyle c}}{\in} \textrm{SampleSpaces}\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Lambda	parameter: 47 body: 2
1	ExprTuple	47
2	Conditional	value: 3 condition: 4
3	Operation	operator: 14 operand: 8
4	Operation	operator: 6 operands: 7
5	ExprTuple	8
6	Literal
7	ExprTuple	47, 9
8	Lambda	parameters: 10 body: 11
9	Literal
10	ExprTuple	76, 77, 67, 46, 74
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operand: 17
13	Operation	operator: 65 operands: 16
14	Literal
15	ExprTuple	17
16	ExprTuple	18, 19, 20
17	Lambda	parameter: 64 body: 22
18	Operation	operator: 23 operands: 24
19	Operation	operator: 30 operands: 25
20	Operation	operator: 26 operands: 34
21	ExprTuple	64
22	Conditional	value: 27 condition: 28
23	Literal
24	ExprTuple	67, 46
25	ExprTuple	67, 29
26	Literal
27	Operation	operator: 30 operands: 31
28	Operation	operator: 72 operands: 32
29	Operation	operator: 33 operands: 34
30	Literal
31	ExprTuple	35, 36
32	ExprTuple	64, 37
33	Literal
34	ExprTuple	76, 77
35	Operation	operator: 50 operand: 43
36	Operation	operator: 39 operands: 40
37	Operation	operator: 41 operands: 42
38	ExprTuple	43
39	Literal
40	ExprTuple	44, 45
41	Literal
42	ExprTuple	46, 47
43	Lambda	parameter: 78 body: 48
44	Operation	operator: 50 operand: 53
45	Operation	operator: 50 operand: 54
46	Variable
47	Variable
48	Conditional	value: 60 condition: 52
49	ExprTuple	53
50	Literal
51	ExprTuple	54
52	Operation	operator: 65 operands: 55
53	Lambda	parameter: 78 body: 56
54	Lambda	parameter: 78 body: 57
55	ExprTuple	58, 70
56	Conditional	value: 60 condition: 59
57	Conditional	value: 60 condition: 61
58	Operation	operator: 72 operands: 62
59	Operation	operator: 65 operands: 63
60	Operation	operator: 64 operand: 78
61	Operation	operator: 65 operands: 66
62	ExprTuple	78, 67
63	ExprTuple	68, 70
64	Variable
65	Literal
66	ExprTuple	69, 70
67	Variable
68	Operation	operator: 72 operands: 71
69	Operation	operator: 72 operands: 73
70	Operation	operator: 74 operand: 78
71	ExprTuple	78, 76
72	Literal
73	ExprTuple	78, 77
74	Variable
75	ExprTuple	78
76	Variable
77	Variable
78	Variable

Expression of type Lambda¶

from the theory of proveit.statistics¶

Expression of type Lambda ¶

from the theory of proveit.statistics ¶