Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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())

\left(\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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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