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, InSet, SetOfAll
from proveit.statistics import Prob, ProbOfAll

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Lambda(f, Conditional(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)), InSet(f, Functions(X, Omega))))

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())

f \mapsto \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) \textrm{ if } f \in \left[X \rightarrow \Omega\right]\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: 5 operand: 8
4	Operation	operator: 34 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	29, 9
8	Lambda	parameter: 36 body: 11
9	Operation	operator: 12 operands: 13
10	ExprTuple	36
11	Operation	operator: 14 operands: 15
12	Literal
13	ExprTuple	38, 16
14	Literal
15	ExprTuple	17, 18
16	Variable
17	Operation	operator: 19 operand: 25
18	Operation	operator: 20 operand: 22
19	Literal
20	Literal
21	ExprTuple	22
22	Operation	operator: 23 operand: 25
23	Literal
24	ExprTuple	25
25	Lambda	parameter: 39 body: 26
26	Conditional	value: 27 condition: 28
27	Operation	operator: 29 operand: 39
28	Operation	operator: 30 operands: 31
29	Variable
30	Literal
31	ExprTuple	32, 33
32	Operation	operator: 34 operands: 35
33	Operation	operator: 36 operand: 39
34	Literal
35	ExprTuple	39, 38
36	Variable
37	ExprTuple	39
38	Variable
39	Variable