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, SubsetEq
from proveit.numbers import LessEq
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = Lambda([A, B], Conditional(LessEq(Prob(A), Prob(B)), And(SubsetEq(A, B), SubsetEq(B, Omega)).with_total_ordering_style()))

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())

\left(A, B\right) \mapsto \left\{\textrm{Pr}\left(A\right) \leq \textrm{Pr}\left(B\right) \textrm{ if } A \subseteq B ,  B \subseteq \Omega\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 15 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11
8	Operation	operator: 13 operand: 18
9	Operation	operator: 13 operand: 19
10	Operation	operator: 16 operands: 15
11	Operation	operator: 16 operands: 17
12	ExprTuple	18
13	Literal
14	ExprTuple	19
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	19, 20
18	Variable
19	Variable
20	Variable