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 Conditional, Lambda, Omega, Q, Qx, X, f, fx, x
from proveit.logic import Equals, Forall, Functions, InClass, SetOfAll
from proveit.statistics import Prob, ProbOfAll, SampleSpaces

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = 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), Prob(SetOfAll(instance_param_or_params = sub_expr1, instance_element = fx, domain = X, condition = Qx))).with_wrapping_at(2)), domain = Functions(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())

\Omega \mapsto \left\{\forall_{X}~\left[\forall_{f \in \left[X \rightarrow \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] =  \\ \textrm{Pr}\left(\left\{f\left(x\right)~|~Q\left(x\right)\right\}_{x \in X}\right) \end{array} \end{array}\right)\right]\right] \textrm{ if } \Omega \underset{{\scriptscriptstyle c}}{\in} \textrm{SampleSpaces}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 29 body: 2
1	ExprTuple	29
2	Conditional	value: 3 condition: 4
3	Operation	operator: 18 operand: 8
4	Operation	operator: 6 operands: 7
5	ExprTuple	8
6	Literal
7	ExprTuple	29, 9
8	Lambda	parameter: 51 body: 11
9	Literal
10	ExprTuple	51
11	Operation	operator: 18 operand: 13
12	ExprTuple	13
13	Lambda	parameter: 42 body: 15
14	ExprTuple	42
15	Conditional	value: 16 condition: 17
16	Operation	operator: 18 operand: 21
17	Operation	operator: 47 operands: 20
18	Literal
19	ExprTuple	21
20	ExprTuple	42, 22
21	Lambda	parameter: 49 body: 24
22	Operation	operator: 25 operands: 26
23	ExprTuple	49
24	Operation	operator: 27 operands: 28
25	Literal
26	ExprTuple	51, 29
27	Literal
28	ExprTuple	30, 31
29	Variable
30	Operation	operator: 32 operand: 38
31	Operation	operator: 33 operand: 35
32	Literal
33	Literal
34	ExprTuple	35
35	Operation	operator: 36 operand: 38
36	Literal
37	ExprTuple	38
38	Lambda	parameter: 52 body: 39
39	Conditional	value: 40 condition: 41
40	Operation	operator: 42 operand: 52
41	Operation	operator: 43 operands: 44
42	Variable
43	Literal
44	ExprTuple	45, 46
45	Operation	operator: 47 operands: 48
46	Operation	operator: 49 operand: 52
47	Literal
48	ExprTuple	52, 51
49	Variable
50	ExprTuple	52
51	Variable
52	Variable