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, Ry, X, f, fx, fy, x, y
from proveit.logic import Bijections, Equals, Forall, Implies, InSet, Not
from proveit.numbers import one, subtract
from proveit.statistics import ProbOfAll

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Conditional(Forall(instance_param_or_params = [Q, R], instance_expr = Implies(Forall(instance_param_or_params = sub_expr1, instance_expr = Equals(Qx, Not(Rx)), domain = X), Equals(ProbOfAll(instance_param_or_params = sub_expr1, instance_element = fx, domain = X, condition = Qx), subtract(one, ProbOfAll(instance_param_or_params = [y], instance_element = fy, domain = X, condition = Ry))).with_wrapping_at(2)).with_wrapping_at(2)), InSet(f, Bijections(X, Omega)))

# 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_{Q, R}~\left(\begin{array}{c} \begin{array}{l} \left[\forall_{x \in X}~\left(Q\left(x\right) = (\lnot R\left(x\right))\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] =  \\ \left(1 - \left[\textrm{Prob}_{y \in X~|~R\left(y\right)}~f\left(y\right)\right]\right) \end{array} \end{array}\right) \end{array} \end{array}\right) \textrm{ if } f \in \left[X \xrightarrow[\text{onto}]{\text{1-to-1}} \Omega\right]\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: 5
2	Operation	operator: 60 operands: 4
3	ExprTuple	5
4	ExprTuple	55, 6
5	Lambda	parameters: 7 body: 8
6	Operation	operator: 9 operands: 10
7	ExprTuple	49, 62
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	64, 13
11	Literal
12	ExprTuple	14, 15
13	Variable
14	Operation	operator: 16 operand: 19
15	Operation	operator: 30 operands: 18
16	Literal
17	ExprTuple	19
18	ExprTuple	20, 21
19	Lambda	parameter: 52 body: 22
20	Operation	operator: 42 operand: 27
21	Operation	operator: 24 operands: 25
22	Conditional	value: 26 condition: 45
23	ExprTuple	27
24	Literal
25	ExprTuple	28, 29
26	Operation	operator: 30 operands: 31
27	Lambda	parameter: 52 body: 32
28	Literal
29	Operation	operator: 33 operand: 38
30	Literal
31	ExprTuple	46, 35
32	Conditional	value: 36 condition: 37
33	Literal
34	ExprTuple	38
35	Operation	operator: 39 operand: 44
36	Operation	operator: 55 operand: 52
37	Operation	operator: 56 operands: 41
38	Operation	operator: 42 operand: 47
39	Literal
40	ExprTuple	44
41	ExprTuple	45, 46
42	Literal
43	ExprTuple	47
44	Operation	operator: 62 operand: 52
45	Operation	operator: 60 operands: 48
46	Operation	operator: 49 operand: 52
47	Lambda	parameter: 65 body: 51
48	ExprTuple	52, 64
49	Variable
50	ExprTuple	52
51	Conditional	value: 53 condition: 54
52	Variable
53	Operation	operator: 55 operand: 65
54	Operation	operator: 56 operands: 57
55	Variable
56	Literal
57	ExprTuple	58, 59
58	Operation	operator: 60 operands: 61
59	Operation	operator: 62 operand: 65
60	Literal
61	ExprTuple	65, 64
62	Variable
63	ExprTuple	65
64	Variable
65	Variable

Expression of type Conditional¶

from the theory of proveit.statistics¶

Expression of type Conditional ¶

from the theory of proveit.statistics ¶