Theorem complementary_event_prob of type Forall

from the theory of proveit.statistics

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.statistics import complementary_event_prob

# check that the built expression is the same as the stored expression
assert complementary_event_prob.expr == stored_expr
assert complementary_event_prob.expr._style_id == stored_expr._style_id
print("Passed sanity check: complementary_event_prob matches stored_expr")

Passed sanity check: complementary_event_prob 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_{S~|~S \subseteq \Omega}~\left(\textrm{Pr}\left(\Omega - S\right) = \left(1 - \textrm{Pr}\left(S\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: 32 body: 4
3	ExprTuple	32
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	32, 12
11	Lambda	parameter: 36 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	36, 32
20	Operation	operator: 34 operand: 25
21	Operation	operator: 23 operands: 24
22	ExprTuple	25
23	Literal
24	ExprTuple	26, 27
25	Operation	operator: 28 operands: 29
26	Literal
27	Operation	operator: 30 operand: 33
28	Literal
29	ExprTuple	32, 36
30	Literal
31	ExprTuple	33
32	Variable
33	Operation	operator: 34 operand: 36
34	Literal
35	ExprTuple	36
36	Variable