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, X, f, fx, x
from proveit.logic import Equals, Forall, InClass, Injections
from proveit.numbers import Sum
from proveit.statistics import Prob, 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], instance_expr = Equals(ProbOfAll(instance_param_or_params = sub_expr1, instance_element = fx, domain = X, condition = Qx), Sum(index_or_indices = sub_expr1, summand = Prob(fx), domain = X, condition = Qx)).with_wrapping_at(2)), domain = Injections(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{1-to-1}} \Omega\right]}~\left[\forall_{Q}~\left(\begin{array}{c} \begin{array}{l} \left[\textrm{Prob}_{x \in X~|~Q\left(x\right)}~f\left(x\right)\right] =  \\ \left[\sum_{x \in X~|~Q\left(x\right)}~\textrm{Pr}\left(f\left(x\right)\right)\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: 30 body: 3
2	ExprTuple	30
3	Conditional	value: 4 condition: 5
4	Operation	operator: 19 operand: 9
5	Operation	operator: 7 operands: 8
6	ExprTuple	9
7	Literal
8	ExprTuple	30, 10
9	Lambda	parameter: 55 body: 12
10	Literal
11	ExprTuple	55
12	Operation	operator: 19 operand: 14
13	ExprTuple	14
14	Lambda	parameter: 50 body: 16
15	ExprTuple	50
16	Conditional	value: 17 condition: 18
17	Operation	operator: 19 operand: 22
18	Operation	operator: 51 operands: 21
19	Literal
20	ExprTuple	22
21	ExprTuple	50, 23
22	Lambda	parameter: 53 body: 25
23	Operation	operator: 26 operands: 27
24	ExprTuple	53
25	Operation	operator: 28 operands: 29
26	Literal
27	ExprTuple	55, 30
28	Literal
29	ExprTuple	31, 32
30	Variable
31	Operation	operator: 33 operand: 37
32	Operation	operator: 35 operand: 38
33	Literal
34	ExprTuple	37
35	Literal
36	ExprTuple	38
37	Lambda	parameter: 56 body: 39
38	Lambda	parameter: 56 body: 40
39	Conditional	value: 47 condition: 42
40	Conditional	value: 41 condition: 42
41	Operation	operator: 43 operand: 47
42	Operation	operator: 45 operands: 46
43	Literal
44	ExprTuple	47
45	Literal
46	ExprTuple	48, 49
47	Operation	operator: 50 operand: 56
48	Operation	operator: 51 operands: 52
49	Operation	operator: 53 operand: 56
50	Variable
51	Literal
52	ExprTuple	56, 55
53	Variable
54	ExprTuple	56
55	Variable
56	Variable