Expression of type ExprTuple

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, ExprTuple, Lambda, Omega, Q, Qx, X, f, fx, x
from proveit.logic import Disjoint, Equals, Forall, InClass, Injections, SubsetEq, Union
from proveit.numbers import Add
from proveit.statistics import ProbOfAll, SampleSpaces

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = ExprTuple(Lambda(Omega, Conditional(Forall(instance_param_or_params = [A, B, C, X, Q], instance_expr = 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)), conditions = [SubsetEq(C, X), Equals(C, Union(A, B)), Disjoint(A, B)]).with_wrapping(), InClass(Omega, SampleSpaces))))

expr:

# 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(\Omega \mapsto \left\{\begin{array}{l}\forall_{A, B, C, X, Q~|~C \subseteq X, C = \left(A \cup B\right), \textrm{disjoint}\left(A, B\right)}~\\
\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)\right]\end{array} \textrm{ if } \Omega \underset{{\scriptscriptstyle c}}{\in} \textrm{SampleSpaces}\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 48 body: 3
2	ExprTuple	48
3	Conditional	value: 4 condition: 5
4	Operation	operator: 15 operand: 9
5	Operation	operator: 7 operands: 8
6	ExprTuple	9
7	Literal
8	ExprTuple	48, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	77, 78, 68, 47, 75
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operand: 18
14	Operation	operator: 66 operands: 17
15	Literal
16	ExprTuple	18
17	ExprTuple	19, 20, 21
18	Lambda	parameter: 65 body: 23
19	Operation	operator: 24 operands: 25
20	Operation	operator: 31 operands: 26
21	Operation	operator: 27 operands: 35
22	ExprTuple	65
23	Conditional	value: 28 condition: 29
24	Literal
25	ExprTuple	68, 47
26	ExprTuple	68, 30
27	Literal
28	Operation	operator: 31 operands: 32
29	Operation	operator: 73 operands: 33
30	Operation	operator: 34 operands: 35
31	Literal
32	ExprTuple	36, 37
33	ExprTuple	65, 38
34	Literal
35	ExprTuple	77, 78
36	Operation	operator: 51 operand: 44
37	Operation	operator: 40 operands: 41
38	Operation	operator: 42 operands: 43
39	ExprTuple	44
40	Literal
41	ExprTuple	45, 46
42	Literal
43	ExprTuple	47, 48
44	Lambda	parameter: 79 body: 49
45	Operation	operator: 51 operand: 54
46	Operation	operator: 51 operand: 55
47	Variable
48	Variable
49	Conditional	value: 61 condition: 53
50	ExprTuple	54
51	Literal
52	ExprTuple	55
53	Operation	operator: 66 operands: 56
54	Lambda	parameter: 79 body: 57
55	Lambda	parameter: 79 body: 58
56	ExprTuple	59, 71
57	Conditional	value: 61 condition: 60
58	Conditional	value: 61 condition: 62
59	Operation	operator: 73 operands: 63
60	Operation	operator: 66 operands: 64
61	Operation	operator: 65 operand: 79
62	Operation	operator: 66 operands: 67
63	ExprTuple	79, 68
64	ExprTuple	69, 71
65	Variable
66	Literal
67	ExprTuple	70, 71
68	Variable
69	Operation	operator: 73 operands: 72
70	Operation	operator: 73 operands: 74
71	Operation	operator: 75 operand: 79
72	ExprTuple	79, 77
73	Literal
74	ExprTuple	79, 78
75	Variable
76	ExprTuple	79
77	Variable
78	Variable
79	Variable