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 Conditional, Omega, Q, Qx, R, Rx, X, f, fx, x
from proveit.logic import Forall, Functions, Implies, InClass
from proveit.numbers import LessEq
from proveit.statistics import ProbOfAll, SampleSpaces

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Conditional(Forall(instance_param_or_params = [X], instance_expr = Forall(instance_param_or_params = [f], instance_expr = Forall(instance_param_or_params = [Q, R], instance_expr = Implies(Forall(instance_param_or_params = sub_expr1, instance_expr = Rx, domain = X, condition = Qx), LessEq(ProbOfAll(instance_param_or_params = sub_expr1, instance_element = fx, domain = X, condition = Qx), ProbOfAll(instance_param_or_params = sub_expr1, instance_element = fx, domain = X, condition = Rx)).with_wrapping_at(2)).with_wrapping_at(2)), domain = Functions(X, Omega)).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\{\forall_{X}~\left[\begin{array}{l}\forall_{f \in \left[X \rightarrow \Omega\right]}~\\
\left[\forall_{Q, R}~\left(\begin{array}{c} \begin{array}{l} \left[\forall_{x \in X~|~Q\left(x\right)}~R\left(x\right)\right] \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \left[\textrm{Prob}_{x \in X~|~Q\left(x\right)}~f\left(x\right)\right] \leq  \\ \left[\textrm{Prob}_{x \in X~|~R\left(x\right)}~f\left(x\right)\right] \end{array} \end{array}\right) \end{array} \end{array}\right)\right]\end{array}\right] \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: 29 operand: 6
2	Operation	operator: 4 operands: 5
3	ExprTuple	6
4	Literal
5	ExprTuple	26, 7
6	Lambda	parameter: 59 body: 9
7	Literal
8	ExprTuple	59
9	Operation	operator: 29 operand: 11
10	ExprTuple	11
11	Lambda	parameter: 48 body: 13
12	ExprTuple	48
13	Conditional	value: 14 condition: 15
14	Operation	operator: 29 operand: 18
15	Operation	operator: 55 operands: 17
16	ExprTuple	18
17	ExprTuple	48, 19
18	Lambda	parameters: 20 body: 21
19	Operation	operator: 22 operands: 23
20	ExprTuple	54, 57
21	Operation	operator: 24 operands: 25
22	Literal
23	ExprTuple	59, 26
24	Literal
25	ExprTuple	27, 28
26	Variable
27	Operation	operator: 29 operand: 33
28	Operation	operator: 31 operands: 32
29	Literal
30	ExprTuple	33
31	Literal
32	ExprTuple	34, 35
33	Lambda	parameter: 60 body: 36
34	Operation	operator: 38 operand: 40
35	Operation	operator: 38 operand: 41
36	Conditional	value: 53 condition: 44
37	ExprTuple	40
38	Literal
39	ExprTuple	41
40	Lambda	parameter: 60 body: 42
41	Lambda	parameter: 60 body: 43
42	Conditional	value: 45 condition: 44
43	Conditional	value: 45 condition: 46
44	Operation	operator: 49 operands: 47
45	Operation	operator: 48 operand: 60
46	Operation	operator: 49 operands: 50
47	ExprTuple	52, 51
48	Variable
49	Literal
50	ExprTuple	52, 53
51	Operation	operator: 54 operand: 60
52	Operation	operator: 55 operands: 56
53	Operation	operator: 57 operand: 60
54	Variable
55	Literal
56	ExprTuple	60, 59
57	Variable
58	ExprTuple	60
59	Variable
60	Variable

Expression of type Conditional¶

from the theory of proveit.statistics¶

Expression of type Conditional ¶

from the theory of proveit.statistics ¶