Expression of type Conditional ¶

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, 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 = 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())

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

Expression of type Conditional¶

from the theory of proveit.statistics¶

Expression of type Conditional ¶

from the theory of proveit.statistics ¶