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, X, f, fx, x
from proveit.logic import Equals, Forall, InClass, Injections
from proveit.numbers import Sum
from proveit.statistics import Prob, 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], instance_expr = Equals(ProbOfAll(instance_param_or_params = sub_expr1, instance_element = fx, domain = X, condition = Qx), Sum(index_or_indices = sub_expr1, summand = Prob(fx), domain = X, condition = Qx)).with_wrapping_at(2)), domain = Injections(X, Omega))), 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[\forall_{f \in \left[X \xrightarrow[]{\text{1-to-1}} \Omega\right]}~\left[\forall_{Q}~\left(\begin{array}{c} \begin{array}{l} \left[\textrm{Prob}_{x \in X~|~Q\left(x\right)}~f\left(x\right)\right] =  \\ \left[\sum_{x \in X~|~Q\left(x\right)}~\textrm{Pr}\left(f\left(x\right)\right)\right] \end{array} \end{array}\right)\right]\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: 16 operand: 6
2	Operation	operator: 4 operands: 5
3	ExprTuple	6
4	Literal
5	ExprTuple	27, 7
6	Lambda	parameter: 52 body: 9
7	Literal
8	ExprTuple	52
9	Operation	operator: 16 operand: 11
10	ExprTuple	11
11	Lambda	parameter: 47 body: 13
12	ExprTuple	47
13	Conditional	value: 14 condition: 15
14	Operation	operator: 16 operand: 19
15	Operation	operator: 48 operands: 18
16	Literal
17	ExprTuple	19
18	ExprTuple	47, 20
19	Lambda	parameter: 50 body: 22
20	Operation	operator: 23 operands: 24
21	ExprTuple	50
22	Operation	operator: 25 operands: 26
23	Literal
24	ExprTuple	52, 27
25	Literal
26	ExprTuple	28, 29
27	Variable
28	Operation	operator: 30 operand: 34
29	Operation	operator: 32 operand: 35
30	Literal
31	ExprTuple	34
32	Literal
33	ExprTuple	35
34	Lambda	parameter: 53 body: 36
35	Lambda	parameter: 53 body: 37
36	Conditional	value: 44 condition: 39
37	Conditional	value: 38 condition: 39
38	Operation	operator: 40 operand: 44
39	Operation	operator: 42 operands: 43
40	Literal
41	ExprTuple	44
42	Literal
43	ExprTuple	45, 46
44	Operation	operator: 47 operand: 53
45	Operation	operator: 48 operands: 49
46	Operation	operator: 50 operand: 53
47	Variable
48	Literal
49	ExprTuple	53, 52
50	Variable
51	ExprTuple	53
52	Variable
53	Variable

Expression of type Conditional¶

from the theory of proveit.statistics¶

Expression of type Conditional ¶

from the theory of proveit.statistics ¶