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, Functions, InClass, SetOfAll
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), Prob(SetOfAll(instance_param_or_params = sub_expr1, instance_element = fx, domain = X, condition = Qx))).with_wrapping_at(2)), domain = Functions(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 \rightarrow \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] =  \\ \textrm{Pr}\left(\left\{f\left(x\right)~|~Q\left(x\right)\right\}_{x \in X}\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: 49 body: 9
7	Literal
8	ExprTuple	49
9	Operation	operator: 16 operand: 11
10	ExprTuple	11
11	Lambda	parameter: 40 body: 13
12	ExprTuple	40
13	Conditional	value: 14 condition: 15
14	Operation	operator: 16 operand: 19
15	Operation	operator: 45 operands: 18
16	Literal
17	ExprTuple	19
18	ExprTuple	40, 20
19	Lambda	parameter: 47 body: 22
20	Operation	operator: 23 operands: 24
21	ExprTuple	47
22	Operation	operator: 25 operands: 26
23	Literal
24	ExprTuple	49, 27
25	Literal
26	ExprTuple	28, 29
27	Variable
28	Operation	operator: 30 operand: 36
29	Operation	operator: 31 operand: 33
30	Literal
31	Literal
32	ExprTuple	33
33	Operation	operator: 34 operand: 36
34	Literal
35	ExprTuple	36
36	Lambda	parameter: 50 body: 37
37	Conditional	value: 38 condition: 39
38	Operation	operator: 40 operand: 50
39	Operation	operator: 41 operands: 42
40	Variable
41	Literal
42	ExprTuple	43, 44
43	Operation	operator: 45 operands: 46
44	Operation	operator: 47 operand: 50
45	Literal
46	ExprTuple	50, 49
47	Variable
48	ExprTuple	50
49	Variable
50	Variable

Expression of type Conditional¶

from the theory of proveit.statistics¶

Expression of type Conditional ¶

from the theory of proveit.statistics ¶