Expression of type Lambda

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 Conditional, Lambda, Omega, S
from proveit.logic import Difference, Equals, SubsetEq
from proveit.numbers import one, subtract
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = Lambda(S, Conditional(Equals(Prob(Difference(Omega, S)), subtract(one, Prob(S))), SubsetEq(S, Omega)))

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())

S \mapsto \left\{\textrm{Pr}\left(\Omega - S\right) = \left(1 - \textrm{Pr}\left(S\right)\right) \textrm{ if } S \subseteq \Omega\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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