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, X
from proveit.logic import Forall, InClass, InSet, SubsetEq
from proveit.statistics import Prob, SampleSpaces, prob_domain

# build up the expression from sub-expressions
expr = Lambda(Omega, Conditional(Forall(instance_param_or_params = [X], instance_expr = InSet(Prob(X), prob_domain), condition = SubsetEq(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~|~X \subseteq \Omega}~\left(\textrm{Pr}\left(X\right) \in \left[0,1\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: 20 body: 2
1	ExprTuple	20
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	20, 10
9	Lambda	parameter: 25 body: 11
10	Literal
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operands: 15
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	25, 20
18	Operation	operator: 21 operand: 25
19	Operation	operator: 23 operands: 24
20	Variable
21	Literal
22	ExprTuple	25
23	Literal
24	ExprTuple	26, 27
25	Variable
26	Literal
27	Literal