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 ExprTuple, Lambda, Omega, x
from proveit.logic import And, Equals, Forall, InClass, InSet
from proveit.numbers import Sum, one
from proveit.statistics import Prob, SampleSpaces, prob_domain

# build up the expression from sub-expressions
sub_expr1 = [x]
sub_expr2 = Prob(x)
expr = ExprTuple(Lambda(Omega, Equals(InClass(Omega, SampleSpaces), And(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(sub_expr2, prob_domain), domain = Omega), Equals(Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = Omega), one))).with_wrapping_at(2)))

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(\begin{array}{c} \begin{array}{l} \left(\Omega \underset{{\scriptscriptstyle c}}{\in} \textrm{SampleSpaces}\right) =  \\ \left(\left[\forall_{x \in \Omega}~\left(\textrm{Pr}\left(x\right) \in \left[0,1\right]\right)\right] \land \left(\left[\sum_{x \in \Omega}~\textrm{Pr}\left(x\right)\right] = 1\right)\right) \end{array} \end{array}\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: 39 body: 3
2	ExprTuple	39
3	Operation	operator: 16 operands: 4
4	ExprTuple	5, 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	39, 11
9	Literal
10	ExprTuple	12, 13
11	Literal
12	Operation	operator: 14 operand: 18
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18
16	Literal
17	ExprTuple	19, 37
18	Lambda	parameter: 38 body: 20
19	Operation	operator: 21 operand: 24
20	Conditional	value: 23 condition: 29
21	Literal
22	ExprTuple	24
23	Operation	operator: 34 operands: 25
24	Lambda	parameter: 38 body: 26
25	ExprTuple	28, 27
26	Conditional	value: 28 condition: 29
27	Operation	operator: 30 operands: 31
28	Operation	operator: 32 operand: 38
29	Operation	operator: 34 operands: 35
30	Literal
31	ExprTuple	36, 37
32	Literal
33	ExprTuple	38
34	Literal
35	ExprTuple	38, 39
36	Literal
37	Literal
38	Variable
39	Variable