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 Lambda, Omega, x
from proveit.logic import And, Equals, Forall, InClass, InSet
from proveit.numbers import Sum, one
from proveit.statistics import Prob, SampleSpaces, prob_domain

# build up the expression from sub-expressions
sub_expr1 = [x]
sub_expr2 = Prob(x)
expr = Lambda(Omega, Equals(InClass(Omega, SampleSpaces), And(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(sub_expr2, prob_domain), domain = Omega), Equals(Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = Omega), one))).with_wrapping_at(2))

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(\begin{array}{c} \begin{array}{l} \left(\Omega \underset{{\scriptscriptstyle c}}{\in} \textrm{SampleSpaces}\right) =  \\ \left(\left[\forall_{x \in \Omega}~\left(\textrm{Pr}\left(x\right) \in \left[0,1\right]\right)\right] \land \left(\left[\sum_{x \in \Omega}~\textrm{Pr}\left(x\right)\right] = 1\right)\right) \end{array} \end{array}\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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