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 Conditional, ExprTuple, Lambda, Omega, Q, Qx, R, Rx, Ry, X, f, fx, fy, x, y
from proveit.logic import Bijections, Equals, Forall, Implies, InClass, Not
from proveit.numbers import one, subtract
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 = [X], instance_expr = Forall(instance_param_or_params = [f], instance_expr = 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)), domain = Bijections(X, Omega))), 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\{\forall_{X}~\left[\forall_{f \in \left[X \xrightarrow[\text{onto}]{\text{1-to-1}} \Omega\right]}~\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)\right]\right] \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: 29 body: 3
2	ExprTuple	29
3	Conditional	value: 4 condition: 5
4	Operation	operator: 32 operand: 9
5	Operation	operator: 7 operands: 8
6	ExprTuple	9
7	Literal
8	ExprTuple	29, 10
9	Lambda	parameter: 80 body: 12
10	Literal
11	ExprTuple	80
12	Operation	operator: 32 operand: 14
13	ExprTuple	14
14	Lambda	parameter: 71 body: 16
15	ExprTuple	71
16	Conditional	value: 17 condition: 18
17	Operation	operator: 32 operand: 21
18	Operation	operator: 76 operands: 20
19	ExprTuple	21
20	ExprTuple	71, 22
21	Lambda	parameters: 23 body: 24
22	Operation	operator: 25 operands: 26
23	ExprTuple	65, 78
24	Operation	operator: 27 operands: 28
25	Literal
26	ExprTuple	80, 29
27	Literal
28	ExprTuple	30, 31
29	Variable
30	Operation	operator: 32 operand: 35
31	Operation	operator: 46 operands: 34
32	Literal
33	ExprTuple	35
34	ExprTuple	36, 37
35	Lambda	parameter: 68 body: 38
36	Operation	operator: 58 operand: 43
37	Operation	operator: 40 operands: 41
38	Conditional	value: 42 condition: 61
39	ExprTuple	43
40	Literal
41	ExprTuple	44, 45
42	Operation	operator: 46 operands: 47
43	Lambda	parameter: 68 body: 48
44	Literal
45	Operation	operator: 49 operand: 54
46	Literal
47	ExprTuple	62, 51
48	Conditional	value: 52 condition: 53
49	Literal
50	ExprTuple	54
51	Operation	operator: 55 operand: 60
52	Operation	operator: 71 operand: 68
53	Operation	operator: 72 operands: 57
54	Operation	operator: 58 operand: 63
55	Literal
56	ExprTuple	60
57	ExprTuple	61, 62
58	Literal
59	ExprTuple	63
60	Operation	operator: 78 operand: 68
61	Operation	operator: 76 operands: 64
62	Operation	operator: 65 operand: 68
63	Lambda	parameter: 81 body: 67
64	ExprTuple	68, 80
65	Variable
66	ExprTuple	68
67	Conditional	value: 69 condition: 70
68	Variable
69	Operation	operator: 71 operand: 81
70	Operation	operator: 72 operands: 73
71	Variable
72	Literal
73	ExprTuple	74, 75
74	Operation	operator: 76 operands: 77
75	Operation	operator: 78 operand: 81
76	Literal
77	ExprTuple	81, 80
78	Variable
79	ExprTuple	81
80	Variable
81	Variable