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 Conditional, ExprTuple, Lambda, Omega, X, x
from proveit.logic import Equals, Forall, InClass, SubsetEq
from proveit.numbers import Sum
from proveit.statistics import Prob, SampleSpaces

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(Omega, Conditional(Forall(instance_param_or_params = [X], instance_expr = Equals(Prob(X), Sum(index_or_indices = [x], summand = Prob(x), domain = X)), 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())

\left(\Omega \mapsto \left\{\forall_{X~|~X \subseteq \Omega}~\left(\textrm{Pr}\left(X\right) = \left[\sum_{x \in X}~\textrm{Pr}\left(x\right)\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: 21 body: 3
2	ExprTuple	21
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	21, 11
10	Lambda	parameter: 34 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	34, 21
19	Operation	operator: 29 operand: 34
20	Operation	operator: 23 operand: 25
21	Variable
22	ExprTuple	34
23	Literal
24	ExprTuple	25
25	Lambda	parameter: 33 body: 26
26	Conditional	value: 27 condition: 28
27	Operation	operator: 29 operand: 33
28	Operation	operator: 31 operands: 32
29	Literal
30	ExprTuple	33
31	Literal
32	ExprTuple	33, 34
33	Variable
34	Variable