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, Qx, X, f, fx, x
from proveit.logic import And, Disjoint, Equals, Forall, Injections, SubsetEq, Union
from proveit.numbers import Add
from proveit.statistics import ProbOfAll

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Conditional(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)), And(SubsetEq(C, X), Equals(C, Union(A, B)), Disjoint(A, B)))

# 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_{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) \textrm{ if } C \subseteq X ,  C = \left(A \cup B\right) ,  \textrm{disjoint}\left(A, B\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: 3 operand: 6
2	Operation	operator: 54 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8, 9
6	Lambda	parameter: 53 body: 11
7	Operation	operator: 12 operands: 13
8	Operation	operator: 19 operands: 14
9	Operation	operator: 15 operands: 23
10	ExprTuple	53
11	Conditional	value: 16 condition: 17
12	Literal
13	ExprTuple	56, 35
14	ExprTuple	56, 18
15	Literal
16	Operation	operator: 19 operands: 20
17	Operation	operator: 61 operands: 21
18	Operation	operator: 22 operands: 23
19	Literal
20	ExprTuple	24, 25
21	ExprTuple	53, 26
22	Literal
23	ExprTuple	65, 66
24	Operation	operator: 39 operand: 32
25	Operation	operator: 28 operands: 29
26	Operation	operator: 30 operands: 31
27	ExprTuple	32
28	Literal
29	ExprTuple	33, 34
30	Literal
31	ExprTuple	35, 36
32	Lambda	parameter: 67 body: 37
33	Operation	operator: 39 operand: 42
34	Operation	operator: 39 operand: 43
35	Variable
36	Variable
37	Conditional	value: 49 condition: 41
38	ExprTuple	42
39	Literal
40	ExprTuple	43
41	Operation	operator: 54 operands: 44
42	Lambda	parameter: 67 body: 45
43	Lambda	parameter: 67 body: 46
44	ExprTuple	47, 59
45	Conditional	value: 49 condition: 48
46	Conditional	value: 49 condition: 50
47	Operation	operator: 61 operands: 51
48	Operation	operator: 54 operands: 52
49	Operation	operator: 53 operand: 67
50	Operation	operator: 54 operands: 55
51	ExprTuple	67, 56
52	ExprTuple	57, 59
53	Variable
54	Literal
55	ExprTuple	58, 59
56	Variable
57	Operation	operator: 61 operands: 60
58	Operation	operator: 61 operands: 62
59	Operation	operator: 63 operand: 67
60	ExprTuple	67, 65
61	Literal
62	ExprTuple	67, 66
63	Variable
64	ExprTuple	67
65	Variable
66	Variable
67	Variable

Expression of type Conditional¶

from the theory of proveit.statistics¶

Expression of type Conditional ¶

from the theory of proveit.statistics ¶