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 A, B, Conditional, Lambda, Omega
from proveit.logic import And, Forall, InClass, SubsetEq
from proveit.numbers import LessEq
from proveit.statistics import Prob, SampleSpaces

# build up the expression from sub-expressions
expr = Lambda(Omega, Conditional(Forall(instance_param_or_params = [A, B], instance_expr = LessEq(Prob(A), Prob(B)), condition = And(SubsetEq(A, B), SubsetEq(B, Omega)).with_total_ordering_style()), 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_{A, B~|~A \subseteq B, B \subseteq \Omega}~\left(\textrm{Pr}\left(A\right) \leq \textrm{Pr}\left(B\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: 30 body: 2
1	ExprTuple	30
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	30, 10
9	Lambda	parameters: 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	20, 21
18	Operation	operator: 23 operand: 28
19	Operation	operator: 23 operand: 29
20	Operation	operator: 26 operands: 25
21	Operation	operator: 26 operands: 27
22	ExprTuple	28
23	Literal
24	ExprTuple	29
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	29, 30
28	Variable
29	Variable
30	Variable