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, x
from proveit.logic import Equals, Forall, SubsetEq
from proveit.numbers import Sum
from proveit.statistics import Prob, SampleSpaces

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [Omega], instance_expr = 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)), domain = 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())

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