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, Forall, InClass, SubsetEq
from proveit.numbers import one, subtract
from proveit.statistics import Prob, SampleSpaces

# build up the expression from sub-expressions
expr = Lambda(Omega, Conditional(Forall(instance_param_or_params = [S], instance_expr = Equals(Prob(Difference(Omega, S)), subtract(one, Prob(S))), condition = SubsetEq(S, Omega)), InClass(Omega, 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())

\Omega \mapsto \left\{\forall_{S~|~S \subseteq \Omega}~\left(\textrm{Pr}\left(\Omega - S\right) = \left(1 - \textrm{Pr}\left(S\right)\right)\right) \textrm{ if } \Omega \underset{{\scriptscriptstyle c}}{\in} \textrm{SampleSpaces}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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