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, Omega, x
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Sum, one
from proveit.statistics import Prob, prob_domain

# build up the expression from sub-expressions
sub_expr1 = [x]
sub_expr2 = Prob(x)
expr = ExprTuple(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))

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(\forall_{x \in \Omega}~\left(\textrm{Pr}\left(x\right) \in \left[0,1\right]\right), \left[\sum_{x \in \Omega}~\textrm{Pr}\left(x\right)\right] = 1\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

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