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 Equals, InSet, Injections
from proveit.numbers import Add
from proveit.statistics import ProbOfAll

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Conditional(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))), InSet(f, Injections(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\{\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) \textrm{ if } f \in \left[X \xrightarrow[]{\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: 3 operands: 4
2	Operation	operator: 43 operands: 5
3	Literal
4	ExprTuple	6, 7
5	ExprTuple	35, 8
6	Operation	operator: 21 operand: 14
7	Operation	operator: 10 operands: 11
8	Operation	operator: 12 operands: 13
9	ExprTuple	14
10	Literal
11	ExprTuple	15, 16
12	Literal
13	ExprTuple	17, 18
14	Lambda	parameter: 49 body: 19
15	Operation	operator: 21 operand: 24
16	Operation	operator: 21 operand: 25
17	Variable
18	Variable
19	Conditional	value: 31 condition: 23
20	ExprTuple	24
21	Literal
22	ExprTuple	25
23	Operation	operator: 36 operands: 26
24	Lambda	parameter: 49 body: 27
25	Lambda	parameter: 49 body: 28
26	ExprTuple	29, 41
27	Conditional	value: 31 condition: 30
28	Conditional	value: 31 condition: 32
29	Operation	operator: 43 operands: 33
30	Operation	operator: 36 operands: 34
31	Operation	operator: 35 operand: 49
32	Operation	operator: 36 operands: 37
33	ExprTuple	49, 38
34	ExprTuple	39, 41
35	Variable
36	Literal
37	ExprTuple	40, 41
38	Variable
39	Operation	operator: 43 operands: 42
40	Operation	operator: 43 operands: 44
41	Operation	operator: 45 operand: 49
42	ExprTuple	49, 47
43	Literal
44	ExprTuple	49, 48
45	Variable
46	ExprTuple	49
47	Variable
48	Variable
49	Variable

Expression of type Conditional¶

from the theory of proveit.statistics¶

Expression of type Conditional ¶

from the theory of proveit.statistics ¶