Expression of type Lambda ¶

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, Lambda, Omega, Q, 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 = Lambda([A, B, C, X, Q], 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(A, B, C, X, Q\right) \mapsto \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	Lambda	parameters: 1 body: 2
1	ExprTuple	67, 68, 58, 37, 65
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 56 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10, 11
8	Lambda	parameter: 55 body: 13
9	Operation	operator: 14 operands: 15
10	Operation	operator: 21 operands: 16
11	Operation	operator: 17 operands: 25
12	ExprTuple	55
13	Conditional	value: 18 condition: 19
14	Literal
15	ExprTuple	58, 37
16	ExprTuple	58, 20
17	Literal
18	Operation	operator: 21 operands: 22
19	Operation	operator: 63 operands: 23
20	Operation	operator: 24 operands: 25
21	Literal
22	ExprTuple	26, 27
23	ExprTuple	55, 28
24	Literal
25	ExprTuple	67, 68
26	Operation	operator: 41 operand: 34
27	Operation	operator: 30 operands: 31
28	Operation	operator: 32 operands: 33
29	ExprTuple	34
30	Literal
31	ExprTuple	35, 36
32	Literal
33	ExprTuple	37, 38
34	Lambda	parameter: 69 body: 39
35	Operation	operator: 41 operand: 44
36	Operation	operator: 41 operand: 45
37	Variable
38	Variable
39	Conditional	value: 51 condition: 43
40	ExprTuple	44
41	Literal
42	ExprTuple	45
43	Operation	operator: 56 operands: 46
44	Lambda	parameter: 69 body: 47
45	Lambda	parameter: 69 body: 48
46	ExprTuple	49, 61
47	Conditional	value: 51 condition: 50
48	Conditional	value: 51 condition: 52
49	Operation	operator: 63 operands: 53
50	Operation	operator: 56 operands: 54
51	Operation	operator: 55 operand: 69
52	Operation	operator: 56 operands: 57
53	ExprTuple	69, 58
54	ExprTuple	59, 61
55	Variable
56	Literal
57	ExprTuple	60, 61
58	Variable
59	Operation	operator: 63 operands: 62
60	Operation	operator: 63 operands: 64
61	Operation	operator: 65 operand: 69
62	ExprTuple	69, 67
63	Literal
64	ExprTuple	69, 68
65	Variable
66	ExprTuple	69
67	Variable
68	Variable
69	Variable

Expression of type Lambda¶

from the theory of proveit.statistics¶

Expression of type Lambda ¶

from the theory of proveit.statistics ¶