Expression of type Forall

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 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 = Forall(instance_param_or_params = [Omega], instance_expr = 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())

\forall_{\Omega}~\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)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 15 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 40 body: 4
3	ExprTuple	40
4	Operation	operator: 17 operands: 5
5	ExprTuple	6, 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	40, 12
10	Literal
11	ExprTuple	13, 14
12	Literal
13	Operation	operator: 15 operand: 19
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19
17	Literal
18	ExprTuple	20, 38
19	Lambda	parameter: 39 body: 21
20	Operation	operator: 22 operand: 25
21	Conditional	value: 24 condition: 30
22	Literal
23	ExprTuple	25
24	Operation	operator: 35 operands: 26
25	Lambda	parameter: 39 body: 27
26	ExprTuple	29, 28
27	Conditional	value: 29 condition: 30
28	Operation	operator: 31 operands: 32
29	Operation	operator: 33 operand: 39
30	Operation	operator: 35 operands: 36
31	Literal
32	ExprTuple	37, 38
33	Literal
34	ExprTuple	39
35	Literal
36	ExprTuple	39, 40
37	Literal
38	Literal
39	Variable
40	Variable