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, X, f, fx, x
from proveit.logic import Forall, Functions, Implies, InClass
from proveit.numbers import LessEq
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 = Rx, domain = X, condition = Qx), LessEq(ProbOfAll(instance_param_or_params = sub_expr1, instance_element = fx, domain = X, condition = Qx), ProbOfAll(instance_param_or_params = sub_expr1, instance_element = fx, domain = X, condition = Rx)).with_wrapping_at(2)).with_wrapping_at(2)), domain = Functions(X, Omega)).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\{\forall_{X}~\left[\begin{array}{l}\forall_{f \in \left[X \rightarrow \Omega\right]}~\\
\left[\forall_{Q, R}~\left(\begin{array}{c} \begin{array}{l} \left[\forall_{x \in X~|~Q\left(x\right)}~R\left(x\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] \leq  \\ \left[\textrm{Prob}_{x \in X~|~R\left(x\right)}~f\left(x\right)\right] \end{array} \end{array}\right) \end{array} \end{array}\right)\right]\end{array}\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: 62 body: 12
10	Literal
11	ExprTuple	62
12	Operation	operator: 32 operand: 14
13	ExprTuple	14
14	Lambda	parameter: 51 body: 16
15	ExprTuple	51
16	Conditional	value: 17 condition: 18
17	Operation	operator: 32 operand: 21
18	Operation	operator: 58 operands: 20
19	ExprTuple	21
20	ExprTuple	51, 22
21	Lambda	parameters: 23 body: 24
22	Operation	operator: 25 operands: 26
23	ExprTuple	57, 60
24	Operation	operator: 27 operands: 28
25	Literal
26	ExprTuple	62, 29
27	Literal
28	ExprTuple	30, 31
29	Variable
30	Operation	operator: 32 operand: 36
31	Operation	operator: 34 operands: 35
32	Literal
33	ExprTuple	36
34	Literal
35	ExprTuple	37, 38
36	Lambda	parameter: 63 body: 39
37	Operation	operator: 41 operand: 43
38	Operation	operator: 41 operand: 44
39	Conditional	value: 56 condition: 47
40	ExprTuple	43
41	Literal
42	ExprTuple	44
43	Lambda	parameter: 63 body: 45
44	Lambda	parameter: 63 body: 46
45	Conditional	value: 48 condition: 47
46	Conditional	value: 48 condition: 49
47	Operation	operator: 52 operands: 50
48	Operation	operator: 51 operand: 63
49	Operation	operator: 52 operands: 53
50	ExprTuple	55, 54
51	Variable
52	Literal
53	ExprTuple	55, 56
54	Operation	operator: 57 operand: 63
55	Operation	operator: 58 operands: 59
56	Operation	operator: 60 operand: 63
57	Variable
58	Literal
59	ExprTuple	63, 62
60	Variable
61	ExprTuple	63
62	Variable
63	Variable